In this manuscript, we define a special type convex function on Euclidean space and explore it on... more In this manuscript, we define a special type convex function on Euclidean space and explore it on the Riemannian manifold. We also detail the fundamental properties of special type convex functions and some examples that illustrate the idea. Moreover, to demonstrate the application to the problems of optimization, these special type convex functions are used.
In the present paper we study Ricci pseudo-symmetry, Z-Ricci pseudo-symmetry and concircularly ps... more In the present paper we study Ricci pseudo-symmetry, Z-Ricci pseudo-symmetry and concircularly pseudo-symmetry conditions on a mixed generalized quasi-Einstein spacetime $ MG(QE)_{4} $. Also, it is proven that if $ d\neq \varLambda $, then $ MG(QE)_{4} $ spacetime does not admit heat flux, where $ d $ and $ \varLambda $ are the function and the cosmological constant, respectively. In the end of this paper we construct a non-trivial example of $ MG(QE)_{4} $ to prove its existence.
In this manuscript, we define a special type convex function on Euclidean space and explore it on... more In this manuscript, we define a special type convex function on Euclidean space and explore it on the Riemannian manifold. We also detail the fundamental properties of special type convex functions and some examples that illustrate the idea. Moreover, to demonstrate the application to the problems of optimization, these special type convex functions are used.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian ma... more In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps: the integrability of distributions, geometry of foliations, the condition for such maps to be totally geodesic, etc. At the end of this article, we give two non-trivial examples of this notion.
In this paper, we study the properties of ϵ-Kenmotsu manifolds if its metrics are *η-Ricci-Yamabe... more In this paper, we study the properties of ϵ-Kenmotsu manifolds if its metrics are *η-Ricci-Yamabe solitons. It is proven that an ϵ-Kenmotsu manifold endowed with a *η-Ricci-Yamabe soliton is η-Einstein. The necessary conditions for an ϵ-Kenmotsu manifold, whose metric is a *η-Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence *η-Ricci-Yamabe solitons.
Using the Newman-Penrose formalism, the Lanczos potential for Petrov type D spacetimes has been f... more Using the Newman-Penrose formalism, the Lanczos potential for Petrov type D spacetimes has been found. It is seen that the Lanczos scalars can be expressed in terms of the spin-coefficients. The non-uniqueness character of the Lanczos potential has been established and a possible justification to the name “the Lanczos potential” is given
Balkan Journal of Geometry and its Applications, 2022
In the present paper, our main objective is to study spacetimes which admit a semiconformal curva... more In the present paper, our main objective is to study spacetimes which admit a semiconformal curvature tensor. First, we prove that the energy-momentum tensor with vanishing semiconformal curvature tensor, satisfying Einstein's field equations (with cosmological constant), is covariantly constant. Next, we prove that if in a perfect fluid spacetime with divergence-free semiconformal curvature tensor satisfying Einstein field equations without cosmological constant, has constant pressure and density. Finally, we prove that if the perfect fluid spacetime has vanishing semiconformal curvature tensor satisfying Einstein field equations without cosmological constant, then the spacetime has constant energy density and isotropic pressure, and the perfect fluid always behaves as having a cosmological constant.
Using the Newman-Penrose formalism, the Lanczos potential for Petrov type D spacetimes has been f... more Using the Newman-Penrose formalism, the Lanczos potential for Petrov type D spacetimes has been found. It is seen that the Lanczos scalars can be expressed in terms of the spin-coefficients. The non-uniqueness character of the Lanczos potential has been established and a possible justification to the name "the Lanczos potential" is given.
In this paper, we study the properties of e-Kenmotsu manifolds if its metrics are ∗η-RicciYamab... more In this paper, we study the properties of e-Kenmotsu manifolds if its metrics are ∗η-RicciYamabe solitons. It is proven that an e-Kenmotsu manifold endowed with a ∗η-Ricci-Yamabe soliton is η-Einstein. The necessary conditions for an e-Kenmotsu manifold, whose metric is a ∗η-RicciYamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence ∗η-Ricci-Yamabe solitons.
In the present article, we introduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian m... more In the present article, we introduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to
Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps:
the integrability of distributions, geometry of foliations, the condition for such maps to be totally
geodesic, etc. At the end of this article, we give two non-trivial examples of this notion.
In this article, we study curvature inheritance symmetry in Ricci flat spacetimes. We show that, ... more In this article, we study curvature inheritance symmetry in Ricci flat spacetimes. We show that, if Ricci flat spacetimes are not of Petrov type N, and admit curvature inheritance symmetries, then the only existing symmetries are conformal motions. We also prove that the only Ricci flat spacetime that admits a proper curvature inheritance symmetry and is of Petrov type other than N is the flat spacetime. Next, we find that the vacuum pp-waves of Petrov type N if admit curvature inheritance symmetry, then conformal motion implies homothetic motion.
The motive of the current article is to study and characterize the geometrical and physical compe... more The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conformal motion and conharmonic motion in general and Einstein spacetime. From the investigation of the kinematical and dynamical properties of the conformal Killing vector (CKV) with the Conh CI vector admitted by spacetime, it is found that they are quite physically applicable in the theory of general relativity. We obtain results on the symmetry inheritance for physical quantities (μ,p,ui,σij,η,qi) of the stress-energy tensor in imperfect fluid, perfect fluid and anisotropic fluid spacetimes. Finally, we prove that the conharmonic curvature tensor of a perfect fluid spacetime will be divergence-free when a Conh CI vector is also a CKV
In this work, we define a v-quasi-bi-slant Riemannian map (in brief, v-QBSR map) from almost Herm... more In this work, we define a v-quasi-bi-slant Riemannian map (in brief, v-QBSR map) from almost Hermitian manifolds to Riemannian manifolds. This notion generalizes both a v-hemi slant Riemannian map and a v-semi slant Riemannian map. The geometry of leaves of distributions that are associated with the definition of such maps is studied. The conditions for v-QBSR maps to be integrable and totally geodesic are also obtained in the paper. Finally, we provide the examples of v-QBSR maps.
International Journal of Theoretical Physics, 2013
The Lanczos potential for an arbitrary Petrov type II spacetime has been obtained and Robinson-Tr... more The Lanczos potential for an arbitrary Petrov type II spacetime has been obtained and Robinson-Trautman family of metrics has been considered as an example.
International Journal of Theoretical Physics, 2011
A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin co... more A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin coefficient formalism (or GHP-formalism), has been obtained; which in turn leads to a solution of Weyl-Lanczos equations.
A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin co... more A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin coefficient formalism (or GHP-formalism), has been obtained; which in turn leads to a solution of Weyl-Lanczos equations.
In this manuscript, we define a special type convex function on Euclidean space and explore it on... more In this manuscript, we define a special type convex function on Euclidean space and explore it on the Riemannian manifold. We also detail the fundamental properties of special type convex functions and some examples that illustrate the idea. Moreover, to demonstrate the application to the problems of optimization, these special type convex functions are used.
In the present paper we study Ricci pseudo-symmetry, Z-Ricci pseudo-symmetry and concircularly ps... more In the present paper we study Ricci pseudo-symmetry, Z-Ricci pseudo-symmetry and concircularly pseudo-symmetry conditions on a mixed generalized quasi-Einstein spacetime $ MG(QE)_{4} $. Also, it is proven that if $ d\neq \varLambda $, then $ MG(QE)_{4} $ spacetime does not admit heat flux, where $ d $ and $ \varLambda $ are the function and the cosmological constant, respectively. In the end of this paper we construct a non-trivial example of $ MG(QE)_{4} $ to prove its existence.
In this manuscript, we define a special type convex function on Euclidean space and explore it on... more In this manuscript, we define a special type convex function on Euclidean space and explore it on the Riemannian manifold. We also detail the fundamental properties of special type convex functions and some examples that illustrate the idea. Moreover, to demonstrate the application to the problems of optimization, these special type convex functions are used.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian ma... more In the present article, we indroduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps: the integrability of distributions, geometry of foliations, the condition for such maps to be totally geodesic, etc. At the end of this article, we give two non-trivial examples of this notion.
In this paper, we study the properties of ϵ-Kenmotsu manifolds if its metrics are *η-Ricci-Yamabe... more In this paper, we study the properties of ϵ-Kenmotsu manifolds if its metrics are *η-Ricci-Yamabe solitons. It is proven that an ϵ-Kenmotsu manifold endowed with a *η-Ricci-Yamabe soliton is η-Einstein. The necessary conditions for an ϵ-Kenmotsu manifold, whose metric is a *η-Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence *η-Ricci-Yamabe solitons.
Using the Newman-Penrose formalism, the Lanczos potential for Petrov type D spacetimes has been f... more Using the Newman-Penrose formalism, the Lanczos potential for Petrov type D spacetimes has been found. It is seen that the Lanczos scalars can be expressed in terms of the spin-coefficients. The non-uniqueness character of the Lanczos potential has been established and a possible justification to the name “the Lanczos potential” is given
Balkan Journal of Geometry and its Applications, 2022
In the present paper, our main objective is to study spacetimes which admit a semiconformal curva... more In the present paper, our main objective is to study spacetimes which admit a semiconformal curvature tensor. First, we prove that the energy-momentum tensor with vanishing semiconformal curvature tensor, satisfying Einstein's field equations (with cosmological constant), is covariantly constant. Next, we prove that if in a perfect fluid spacetime with divergence-free semiconformal curvature tensor satisfying Einstein field equations without cosmological constant, has constant pressure and density. Finally, we prove that if the perfect fluid spacetime has vanishing semiconformal curvature tensor satisfying Einstein field equations without cosmological constant, then the spacetime has constant energy density and isotropic pressure, and the perfect fluid always behaves as having a cosmological constant.
Using the Newman-Penrose formalism, the Lanczos potential for Petrov type D spacetimes has been f... more Using the Newman-Penrose formalism, the Lanczos potential for Petrov type D spacetimes has been found. It is seen that the Lanczos scalars can be expressed in terms of the spin-coefficients. The non-uniqueness character of the Lanczos potential has been established and a possible justification to the name "the Lanczos potential" is given.
In this paper, we study the properties of e-Kenmotsu manifolds if its metrics are ∗η-RicciYamab... more In this paper, we study the properties of e-Kenmotsu manifolds if its metrics are ∗η-RicciYamabe solitons. It is proven that an e-Kenmotsu manifold endowed with a ∗η-Ricci-Yamabe soliton is η-Einstein. The necessary conditions for an e-Kenmotsu manifold, whose metric is a ∗η-RicciYamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence ∗η-Ricci-Yamabe solitons.
In the present article, we introduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian m... more In the present article, we introduce and study h-quasi-hemi-slant (in short, h-qhs) Riemannian maps and almost h-qhs Riemannian maps from almost quaternionic Hermitian manifolds to
Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps:
the integrability of distributions, geometry of foliations, the condition for such maps to be totally
geodesic, etc. At the end of this article, we give two non-trivial examples of this notion.
In this article, we study curvature inheritance symmetry in Ricci flat spacetimes. We show that, ... more In this article, we study curvature inheritance symmetry in Ricci flat spacetimes. We show that, if Ricci flat spacetimes are not of Petrov type N, and admit curvature inheritance symmetries, then the only existing symmetries are conformal motions. We also prove that the only Ricci flat spacetime that admits a proper curvature inheritance symmetry and is of Petrov type other than N is the flat spacetime. Next, we find that the vacuum pp-waves of Petrov type N if admit curvature inheritance symmetry, then conformal motion implies homothetic motion.
The motive of the current article is to study and characterize the geometrical and physical compe... more The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conformal motion and conharmonic motion in general and Einstein spacetime. From the investigation of the kinematical and dynamical properties of the conformal Killing vector (CKV) with the Conh CI vector admitted by spacetime, it is found that they are quite physically applicable in the theory of general relativity. We obtain results on the symmetry inheritance for physical quantities (μ,p,ui,σij,η,qi) of the stress-energy tensor in imperfect fluid, perfect fluid and anisotropic fluid spacetimes. Finally, we prove that the conharmonic curvature tensor of a perfect fluid spacetime will be divergence-free when a Conh CI vector is also a CKV
In this work, we define a v-quasi-bi-slant Riemannian map (in brief, v-QBSR map) from almost Herm... more In this work, we define a v-quasi-bi-slant Riemannian map (in brief, v-QBSR map) from almost Hermitian manifolds to Riemannian manifolds. This notion generalizes both a v-hemi slant Riemannian map and a v-semi slant Riemannian map. The geometry of leaves of distributions that are associated with the definition of such maps is studied. The conditions for v-QBSR maps to be integrable and totally geodesic are also obtained in the paper. Finally, we provide the examples of v-QBSR maps.
International Journal of Theoretical Physics, 2013
The Lanczos potential for an arbitrary Petrov type II spacetime has been obtained and Robinson-Tr... more The Lanczos potential for an arbitrary Petrov type II spacetime has been obtained and Robinson-Trautman family of metrics has been considered as an example.
International Journal of Theoretical Physics, 2011
A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin co... more A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin coefficient formalism (or GHP-formalism), has been obtained; which in turn leads to a solution of Weyl-Lanczos equations.
A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin co... more A Lanczos potential for an arbitrary Petrov type D vacuum spacetimes, using the compacted spin coefficient formalism (or GHP-formalism), has been obtained; which in turn leads to a solution of Weyl-Lanczos equations.
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Papers by Mohd Bilal
is η-Einstein. The necessary conditions for an e-Kenmotsu manifold, whose metric is a ∗η-RicciYamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu
manifold example of dimension 5 to examine the existence ∗η-Ricci-Yamabe solitons.
Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps:
the integrability of distributions, geometry of foliations, the condition for such maps to be totally
geodesic, etc. At the end of this article, we give two non-trivial examples of this notion.
is η-Einstein. The necessary conditions for an e-Kenmotsu manifold, whose metric is a ∗η-RicciYamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu
manifold example of dimension 5 to examine the existence ∗η-Ricci-Yamabe solitons.
Riemannian manifolds. We investigate some fundamental results mainly on h-qhs Riemannian maps:
the integrability of distributions, geometry of foliations, the condition for such maps to be totally
geodesic, etc. At the end of this article, we give two non-trivial examples of this notion.