Papers by Dr. V. K. Chaubey
Locally dually flatness properties in cubic $ (\alpha, \beta) $-Metric
Mathematical foundations of computing, 2024
arXiv: Differential Geometry, 2015
In the year 1984 Shibata investigated the theory of a change which is called a �-change of a Fins... more In the year 1984 Shibata investigated the theory of a change which is called a �-change of a Finsler metric. On the other hand in 1985 a systematic study of geometry of hypersurfaces in Finsler spaces was given by Matsumoto. In the present paper is to devoted to the study of a condition for a Randers conformal change to be projective and find out when a totally geodesic hypersurface F n 1 remains to be a totally geodesic hypersurface F n 1 under the projective Randers conformal change. Further obatined the condition under which a Finslerian hypersurfaces given by the projective Randers conformal change are projectively flat.
Differential geometry of special Finsler spaces of special metric
Theory of Finsler Spaces with (Γ, Β) Metrics
Bulletin of the Transilvania …, 2011
... Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur (UP)-273009, INDIA, E-mail:- ... more ... Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur (UP)-273009, INDIA, E-mail:- vkcoct@gmail.com 1Author is very thankful to NBHM-DAE of Goverment of INDIA for their financial assistance as a Postdoctoral Fellowship Page 2. 44 TN Pandey and VK Chaubey ...
Equation of Geodesic for a (Α, Β)-Metric in a Two-Dimensional Finsler Space
researchgate.net
... 143-150 143 EQUATION OF GEODESIC FOR A (α, β)- METRIC IN A TWO-DIMENSIONAL FINSLER SPACE VK C... more ... 143-150 143 EQUATION OF GEODESIC FOR A (α, β)- METRIC IN A TWO-DIMENSIONAL FINSLER SPACE VK Chaubey, DD Tripathi, BN Prasad Department of Mathematics Statistics, DDU Gorakhpur University, Gorakhpur (UP), India vkcoct@rediffmail.com ...
On Finsler Spaces with a Quartic Metric
Journal of the Tensor Society, Nov 30, 2008
ABSTRACT The purpose of the present paper is to study spaces with a quartic metric from the stand... more ABSTRACT The purpose of the present paper is to study spaces with a quartic metric from the standpoint of Finsler geometry. The paper deals with Berwald and Landsberg spaces among quartic Finsler spaces. A Finsler connection is defined in a quartic Finsler space from the standpoint of the generalized metric space.
The purpose of the present paper is to obtain the relation between imbedding class numbers of tan... more The purpose of the present paper is to obtain the relation between imbedding class numbers of tangent Riemannian spaces.
M Th-Root Randers Change Of A Finsler Metric
In the year 1979, Shimada introduced the concept of m<sup>th</sup> root metric and de... more In the year 1979, Shimada introduced the concept of m<sup>th</sup> root metric and developed it as an interesting example of Finsler metrics, immediately following M.Matsumoto and S.Numatas theory of cubic metrics. By introducing the regularity of the metric various fundamental quantities as a Finsler metric could be found.
Finslerian hypersurfaces of a Finsler space with deformed randers $(\alpha,\beta)$- metric
Novi Sad Journal of Mathematics, 2022
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2017
In the present paper we study the Finslerian hypersurfaces of a Finsler space with a special (α, ... more In the present paper we study the Finslerian hypersurfaces of a Finsler space with a special (α, β) metric, and examine the hypersurfaces of this special metric as a hyperplane of first, second and third kinds.
arXiv: General Mathematics, 2015
In the present paper we have considered h-Randers conformal change of a Finsler metric $ L $, whi... more In the present paper we have considered h-Randers conformal change of a Finsler metric $ L $, which is defined as \begin{center}$ L(x,y)\rightarrow \bar{L}(x, y)=e^{\sigma(x)}L(x, y)+\beta (x, y), \end{center} where $ \sigma(x) $ is a function of x, $\beta(x, y) = b_{i}(x, y)y^{i}$ is a 1- form on $M^{n}$ and $b_{i}$ satisfies the condition of being an h-vector. We have obtained the expressions for geodesic spray coefficients under this change. Further we have studied some special Finsler spaces namely quasi-C-reducible, C-reducible, S3-like and S4-like Finsler spaces arising from this metric. We have also obtained the condition under which this change of metric leads a Berwald (or a Landsberg) space into a space of the same kind.
Scalar curvature of two-dimensional Finsler spaces with (α,β)-Metric
In the present paper we have obtain scalar curvature R of Two-dimensional Finsler space with (α,β... more In the present paper we have obtain scalar curvature R of Two-dimensional Finsler space with (α,β)-metric. Some special (α,β)-metric such as Randers metric, Kropina metric, Generalized Kropina metric and Matsumoto metric have also been considered and explicit expression for scalar curvature R has been find out.
Theory of Finsler spaces with (gamma, beta)-metric
In the present paper, we introduce the concept of (γ, β)-metric and a number of propositions and ... more In the present paper, we introduce the concept of (γ, β)-metric and a number of propositions and theorems have worked for a (γ, β)-metric, where γ3 = aijk(x)yiyjyk is a cubic metric and β = bi(x)yi is a one form metric
A Finsler space is said to be a generalized C v -reducible Finsler space if C ijk | h can be writ... more A Finsler space is said to be a generalized C v -reducible Finsler space if C ijk | h can be written as a product of tensors of type (0,3) and (0,1) such as, LC ijk | h =A ijk B h +A ijh B k +A ihk B j +A hjk B i ,A ijk ≠λC ijk , where A i00 =0,A ij0 ≠0andB 0 =0A i00 =A ijk y j y k ,B 0 =B i y i · In the present paper, we determine the value of A ijk , setting B i =m i , respectively, B i =n i , where m i =C i /C and n i is the unit vector perpendicular to the plane spanned by l i and m i .
On Four-dimensional Finsler spaces with cubic metric
In the year 1997 and 1998 Matsumoto And Park obtained the equations of geodesic in a two-dimensio... more In the year 1997 and 1998 Matsumoto And Park obtained the equations of geodesic in a two-dimensional Randers, Kropina and Matsumoto space. In 2011, Chaubey, Prasad and Tripathi obtained the equation of geodesic for a more general (alpha, beta)-metric as compared to Randers, Kropina and Matsumoto mertric. In the continuation of the above paper, here we have found out the equation of geodesic for the well known metric� and the main results are illustrated in the different figures.
Landsberg and Berwald spaces of dimensions two with generalized (α,β)-Metric
M. Matsumoto introduced the concept of (α,β)-metric in the year, 1972. We have in 1999, the conce... more M. Matsumoto introduced the concept of (α,β)-metric in the year, 1972. We have in 1999, the concept of generalized (α,β)-metric by taking L(α,β^(1)),β^(2)),…….,β^(m))) as homogeneous function of degree one in α,β^(1)),β^(2)),…….,β^(m)) where α=√(a_ij (x)y^i y^j ) is a purely Riemannian metric and 〖 β〗^(1)),β^(2)),…….,β^(m)) all are one-form (β^(r))=b_i^(r)) y^i). In the present paper, we had studied the condition under which a two-dimensional generalized (α,β)-metric be a Landsberg and Berwald spaces in which the main scalar I plays an important role.
Generalized Cv-reducible Finsler spaces
In 1984, C. Shibata studied properties of Finsler spaces (M n ,L * ) whose fundamental metric fun... more In 1984, C. Shibata studied properties of Finsler spaces (M n ,L * ) whose fundamental metric function L * (x,y) is obtained from L by the relation L * (x,y)=f(L,β), where f is a positively homogeneous function of degree one in L and β. This change of Finsler metric function was called a β-change. The geometry of a Lagrange space over a real, finite-dimensional manifold M has been introduced and studied as a sub-geometry of the geometry of the tangent bundle TM by R. Miron. In the present paper we study Lagrange spaces due to β-change and obtain fundamental tensor fields for these spaces and also the variational problem of Lagrange spaces. The results follow the classical ones and some results of R. Miron concerning Lagrange spaces.
International Journal of Pure and Apllied Mathematics, 2013
In the present paper we have studied the Finslerian hypersurfaces and Randers conformal change of... more In the present paper we have studied the Finslerian hypersurfaces and Randers conformal change of a Finsler metric. The relations between the Finslerian hypersurface and the other which is Finslerian hypersurface given by Randers conformal change have been obtained. We have also proved that Randers conformal change makes three types of hypersurfaces invariant under certain condition. These three types of hypersurfaces are hyperplanes of first, second and third kind.
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Papers by Dr. V. K. Chaubey