FINSLER SPACE SUBJECTED TO A KROPINA CHANGE WITH AN h-VECTOR

Manish Kumar Gupta, Paras Nath Pandey

DOI Number
-
First page
513
Last page
525

Abstract


In this paper, we discuss the Finsler spaces $(M^n,L)$ and $(M^n,\,^{*}L)$, where $^{*}L(x,y)$ is obtained from $L(x,y)$ by Kropina change $^{*}L(x,y)=\frac{L^2(x,y)}{b_i(x,y)\,y^i}$ and $b^{}_{i}(x,y)$ is an \textsl{h}-vector in $(M^n,L)$. We find the necessary and sufficient condition when the Cartan connection coefficients for both spaces $(M^n,L)$ and $(M^n,\,^{*}L)$ are the same. We also find the necessary and sufficient condition for Kropina change with an \textsl{h}-vector to be projective.

Keywords


Finsler space, Kropina change, \textsl{h}-vector.

Full Text:

PDF

References


bibitem[1]{An93} P. L. Antonelli, R. S. Ingarden and M. Matsumoto, textit{The theory of Sprays and Finsler spaces with applications in Physics and Biology}, Kluwer Acad. Publishers, Dordrecht / Boston / London, 1993.

bibitem[2]{An12} P. L. Antonelli, S. F. Rutz and K. T. Fonseca, The mathematical theory of endosymbiosis, II: Models of the Fungal Fusion hypothesis, textit{Nonlinear Analysis RWA}, textbf{13} (2012) 2096-2103.

bibitem[3]{As85} G. S. Asanov, textit{Finsler Geometry, Relativity and Gauge Theories} D. Reidel Publishing Company, Dordrecht, Holland, 1985.

bibitem[4]{GuPa09} M. K. Gupta and P. N. Pandey, Hypersurfaces of conformally and h-conformally related Finsler spaces, textit{Acta Math. Hungar.} textbf{123(3)} (2009), 257-264.

bibitem[5]{GuPa08} M. K. Gupta and P. N. Pandey, On hypersurface of a Finsler space with a special metric, textit{Acta Math. Hungar.} textbf{120(1-2)} (2008), 165-177.

bibitem[6]{In87} R. S. Ingarden, textit{Geometry of thermodynamics} Diff. Geom. Methods in Ther. Phys. (ed. H.D. Doebner et al.), XV Intern. Conf. Clausthal 1986, World Scientific, Singapore, 1987.

bibitem[7]{Iz80} H. Izumi, Conformal transformations of Finsler spaces II. An textsl{h}-conformally flat Finsler space, textit{Tensor N.S.} textbf{34} (1980), 337-359.

bibitem[8]{Kr59} V. K. Kropina, On projective Finsler spaces with a certain special form, textit{Nauv{c}n Doklady vyss. Skoly, fiz.-mat. Nauki} 1959(2) (1960), 38-42 (in Russian).

bibitem[9]{Kr61} V. K. Kropina, On projective two-dimensional Finsler spaces with special metric, textit{Trudy Sem. Vektor. Tenzor. Anal.} textbf{11} (1961), 277-292 (in Russian).

bibitem[10]{Ma72} M. Matsumoto, On C-reducible Finsler spaces, textit{Tensor N.S.} textbf{24} (1972), 29-37.

bibitem[11]{Ma74} M. Matsumoto, On Finsler spaces with Randers metric and special forms of special tensors, textit{J. Math. Kyoto Univ.} textbf{14-3} (1974), 477-498.

bibitem[12]{Ma91} M. Matsumoto, Finsler spaces of constant curvature with Kropina metric, textit{Tensor N.S.} textbf{50} (1991), 194-201.

bibitem[13]{Ma92} M. Matsumoto, Theory of Finsler spaces with $(alpha,beta)$-metric, textit{Rep. Math. Phys.} textbf{31-1} (1992), 43-83.

bibitem[14]{Pr90} B.N. Prasad, On the torsion tensors $R_{hjk}$ and $P_{hjk}$ of Finsler spaces with a metric $ds=(g_{ij}(dx),dx^{i},dx^{j})^{1/2}+b_{i}(x,y),dx^{i}$, textit{Indian J. pure appl. Math. } textbf{21-1} (1990), 27-39.

bibitem[15]{Sh78} C. Shibata, On Finsler spaces with Kropina metric, textit{Rep. Math. Phys.} textbf{13} (1978), 117-128.

bibitem[16]{Sh84} C. Shibata, On invariant tensors of $beta$-changes of Finsler metric, textit{J. Math. Kyoto Univ.} textbf{24-1} (1984), 163-188.


Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)