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
For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and suf... more For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has a Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future-pointing time-like vectors is ensured. The identified (α,β)-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an (α,β)-metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all (α,β)-metrics which admit isometries that are not isometries of a.
For the general class of pseudo-Finsler spaces with (α, β)-metrics, we establish necessary and su... more For the general class of pseudo-Finsler spaces with (α, β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future pointing timelike vectors is ensured. The identified (α, β)-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an (α, β)-metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all (α, β)-metrics which admit isometries that are not isometries of a.
In this paper is studied the differential geometry of the complex indicatrix, which is approached... more In this paper is studied the differential geometry of the complex indicatrix, which is approached as an embedded CR hypersurface of the punctual holomorphic tangent bundle of a complex Finsler space. Following the study of CR submanifolds of a Kähler manifold and using the submanifold formulae there are investigated some properties of the complex indicatrix, such as the fact that it is an extrinsic hypersphere of the holomorphic tangent space. The fundamental equations of the indicatrix as a real submanifold of codimension 1 are also determined. Besides this, the CR-structure integrability is studied and the Levi form and characteristic direction of the complex indicatrix are given. AMS Mathematics Subject Classification (2010): 53B40, 53C60, 53C40, 53B25.
Following the study of the indicatrix of a real Finsler space, in this paper there are investigat... more Following the study of the indicatrix of a real Finsler space, in this paper there are investigated some properties of the complex indicatrix of a complex Finsler space, both in a fixed point and for the indicatrix bundle. In a fixed point z0 ∈ M , the associated indicatrix Iz0M is a convex hypersurface in the holomorphic tangent space T ′ z0M and it can be regarded as a locally Minkowski manifold. Using the submanifold equations, several properties of the indicatrix in a fixed point are obtained in terms of the fundamental function. In the global case, an almost contact structure is introduced on the indicatrix bundle and considering the Gauss-Weingarten equations with respect to the Chern-Finsler connection, a constant value of the mean curvature is determined.
Following the study of real hypersurfaces of Finsler spaces, in this paper we analyse the holomor... more Following the study of real hypersurfaces of Finsler spaces, in this paper we analyse the holomorphic hypersurfaces associated to a complex Finsler space (M,F ) as holomorphic subspaces of complex codimension one. In this sense the induced complex Finsler metric, the induced nonlinear connection and, respectively, the linear connection and the equations of the holomorphic curvature are investigated. Moreover, based on the Gauss, Codazzi and Ricci equations we find the link between the holomorphic curvatures of the holomorphic hypersurface and the Finsler space (M,F ), and the conditions under which the holomorphic hypersurface is totally geodesic, c-totally geodesic or generalized Einstein. 2000 Mathematics Subject Classification: 32C10, 53C60, 53C40, 53B40
Following the study of the indicatrix of a complex Finsler space (M;L) initiated in [10], in this... more Following the study of the indicatrix of a complex Finsler space (M;L) initiated in [10], in this paper an adapted frame is introduced on the complexied of the real tangent bundle of the complex Finsler manifold in a manner that makes it easier to study the properties of the indicatrix bundle. The indicatrix IM is studied as a hypersurface of the holomorphic tangent bundle T 0 M and the adapted frame obtained on it gives simplied expressions of
Following the study on volume of indicatrices in a real Finsler space, in this paper we are inves... more Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume element of the indicatrix is determined. Thus, the volume function is pointed out and its variation is studied. Conditions under which the volume is constant are also determined and some classes of complex Finsler spaces with constant indicatrix volume are given. Moreover, the length of the complex indicatrix of Riemann surfaces is found to be constant. In addition, considering submersions from the complex indicatrix onto almost Hermitian surfaces, we obtain that the volume of the submersed manifold is constant.
In this paper we extend the study of the indicatrix of a complex Finsler space initiated in [10, ... more In this paper we extend the study of the indicatrix of a complex Finsler space initiated in [10, 11]. The equations that can be introduced on the indicatrix, which is studied as a hypersurface of a complex Finsler space, are investigated. In this manner, using the equations of Gauss-Weingarten, the link between the intrinsic and induced connection is deduced. The equations of Gauss, Hand A-Codazzi, and Ricci equations of the indicatrix are considered. Also, conditions for totally umbilical indicatrix are obtained.
Continuing the study of the complex indicatrix IzM , approached as an embedded CR hypersurface on... more Continuing the study of the complex indicatrix IzM , approached as an embedded CR hypersurface on the punctual holomorphic tangent bundle of a complex Finsler space, we study in this paper the almost contact structures that can be introduced on IzM . The Levi form and characteristic direction of the complex indicatrix are given and the CR distributions integrability is studied. Using these we construct a natural contact structure subordonated to the CR-structure of the complex indicatrix, which is also normal. Moreover, with respect to the natural contact structure, the associated connections on IzM , such as Tanaka and Tanaka Webster connections, are determined and the Bochner type tensor field of the complex indicatrix is introduced. M.S.C. 2010: 53B40, 53C60, 53C40, 53B25.
In this paper we study the differential geometry of the complex indicatrix, which is approached a... more In this paper we study the differential geometry of the complex indicatrix, which is approached as an embedded CR hypersurface of the punctual holomorphic tangent bundle of a complex Finsler space. Following the study of CR submanifolds of a Kähler manifold and using the submanifold formulae we investigate some properties of the complex indicatrix, such as the fact that it is an extrinsic hypersphere of the holomorphic tangent space. The fundamental equations of the indicatrix as a real submanifold of codimension 1 are also determined. Besides this, the CR-structure integrability is studied and the Levi form and characteristic direction of the complex indicatrix are given.
Analele Universitatii "Ovidius" Constanta - Seria Matematica
By regarding the complex indicatrix as an embedded CR-hypersurface of the holomorphic tangent bun... more By regarding the complex indicatrix as an embedded CR-hypersurface of the holomorphic tangent bundle in a fixed point, we analyze some aspects of the relations between its CR structure and the considered contact structure. Moreover, using the classification of the almost contact metric structures associated with a strongly pseudo-convex CR-structure, of D. Chinea and C. Gonzales, we determine the classes corresponding to the natural contact structure of the complex indicatrix and the new structures obtained under a gauge transformation.
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
For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and suf... more For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has a Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future-pointing time-like vectors is ensured. The identified (α,β)-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an (α,β)-metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all (α,β)-metrics which admit isometries that are not isometries of a.
For the general class of pseudo-Finsler spaces with (α, β)-metrics, we establish necessary and su... more For the general class of pseudo-Finsler spaces with (α, β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future pointing timelike vectors is ensured. The identified (α, β)-Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an (α, β)-metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all (α, β)-metrics which admit isometries that are not isometries of a.
In this paper is studied the differential geometry of the complex indicatrix, which is approached... more In this paper is studied the differential geometry of the complex indicatrix, which is approached as an embedded CR hypersurface of the punctual holomorphic tangent bundle of a complex Finsler space. Following the study of CR submanifolds of a Kähler manifold and using the submanifold formulae there are investigated some properties of the complex indicatrix, such as the fact that it is an extrinsic hypersphere of the holomorphic tangent space. The fundamental equations of the indicatrix as a real submanifold of codimension 1 are also determined. Besides this, the CR-structure integrability is studied and the Levi form and characteristic direction of the complex indicatrix are given. AMS Mathematics Subject Classification (2010): 53B40, 53C60, 53C40, 53B25.
Following the study of the indicatrix of a real Finsler space, in this paper there are investigat... more Following the study of the indicatrix of a real Finsler space, in this paper there are investigated some properties of the complex indicatrix of a complex Finsler space, both in a fixed point and for the indicatrix bundle. In a fixed point z0 ∈ M , the associated indicatrix Iz0M is a convex hypersurface in the holomorphic tangent space T ′ z0M and it can be regarded as a locally Minkowski manifold. Using the submanifold equations, several properties of the indicatrix in a fixed point are obtained in terms of the fundamental function. In the global case, an almost contact structure is introduced on the indicatrix bundle and considering the Gauss-Weingarten equations with respect to the Chern-Finsler connection, a constant value of the mean curvature is determined.
Following the study of real hypersurfaces of Finsler spaces, in this paper we analyse the holomor... more Following the study of real hypersurfaces of Finsler spaces, in this paper we analyse the holomorphic hypersurfaces associated to a complex Finsler space (M,F ) as holomorphic subspaces of complex codimension one. In this sense the induced complex Finsler metric, the induced nonlinear connection and, respectively, the linear connection and the equations of the holomorphic curvature are investigated. Moreover, based on the Gauss, Codazzi and Ricci equations we find the link between the holomorphic curvatures of the holomorphic hypersurface and the Finsler space (M,F ), and the conditions under which the holomorphic hypersurface is totally geodesic, c-totally geodesic or generalized Einstein. 2000 Mathematics Subject Classification: 32C10, 53C60, 53C40, 53B40
Following the study of the indicatrix of a complex Finsler space (M;L) initiated in [10], in this... more Following the study of the indicatrix of a complex Finsler space (M;L) initiated in [10], in this paper an adapted frame is introduced on the complexied of the real tangent bundle of the complex Finsler manifold in a manner that makes it easier to study the properties of the indicatrix bundle. The indicatrix IM is studied as a hypersurface of the holomorphic tangent bundle T 0 M and the adapted frame obtained on it gives simplied expressions of
Following the study on volume of indicatrices in a real Finsler space, in this paper we are inves... more Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume element of the indicatrix is determined. Thus, the volume function is pointed out and its variation is studied. Conditions under which the volume is constant are also determined and some classes of complex Finsler spaces with constant indicatrix volume are given. Moreover, the length of the complex indicatrix of Riemann surfaces is found to be constant. In addition, considering submersions from the complex indicatrix onto almost Hermitian surfaces, we obtain that the volume of the submersed manifold is constant.
In this paper we extend the study of the indicatrix of a complex Finsler space initiated in [10, ... more In this paper we extend the study of the indicatrix of a complex Finsler space initiated in [10, 11]. The equations that can be introduced on the indicatrix, which is studied as a hypersurface of a complex Finsler space, are investigated. In this manner, using the equations of Gauss-Weingarten, the link between the intrinsic and induced connection is deduced. The equations of Gauss, Hand A-Codazzi, and Ricci equations of the indicatrix are considered. Also, conditions for totally umbilical indicatrix are obtained.
Continuing the study of the complex indicatrix IzM , approached as an embedded CR hypersurface on... more Continuing the study of the complex indicatrix IzM , approached as an embedded CR hypersurface on the punctual holomorphic tangent bundle of a complex Finsler space, we study in this paper the almost contact structures that can be introduced on IzM . The Levi form and characteristic direction of the complex indicatrix are given and the CR distributions integrability is studied. Using these we construct a natural contact structure subordonated to the CR-structure of the complex indicatrix, which is also normal. Moreover, with respect to the natural contact structure, the associated connections on IzM , such as Tanaka and Tanaka Webster connections, are determined and the Bochner type tensor field of the complex indicatrix is introduced. M.S.C. 2010: 53B40, 53C60, 53C40, 53B25.
In this paper we study the differential geometry of the complex indicatrix, which is approached a... more In this paper we study the differential geometry of the complex indicatrix, which is approached as an embedded CR hypersurface of the punctual holomorphic tangent bundle of a complex Finsler space. Following the study of CR submanifolds of a Kähler manifold and using the submanifold formulae we investigate some properties of the complex indicatrix, such as the fact that it is an extrinsic hypersphere of the holomorphic tangent space. The fundamental equations of the indicatrix as a real submanifold of codimension 1 are also determined. Besides this, the CR-structure integrability is studied and the Levi form and characteristic direction of the complex indicatrix are given.
Analele Universitatii "Ovidius" Constanta - Seria Matematica
By regarding the complex indicatrix as an embedded CR-hypersurface of the holomorphic tangent bun... more By regarding the complex indicatrix as an embedded CR-hypersurface of the holomorphic tangent bundle in a fixed point, we analyze some aspects of the relations between its CR structure and the considered contact structure. Moreover, using the classification of the almost contact metric structures associated with a strongly pseudo-convex CR-structure, of D. Chinea and C. Gonzales, we determine the classes corresponding to the natural contact structure of the complex indicatrix and the new structures obtained under a gauge transformation.
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