HYPERSURFACES OF A FINSLER SPACE WITH PROJECTIVE GENERALIZED KROPINA CONFORMAL CHANGE METRIC

Akansha Shukla, Prachi N. Pandey

DOI Number
10.22190/FUMI1705763S
First page
763
Last page
779

Abstract


In the present paper, we have studied a Finsler space whose metric is obtained from the metric of a Finsler space by generalized Kropina conformal change and obtained a necessary and sufficient condition for these Finsler spaces to be projectively related. Apart from other results, the relation between the hypersurfaces of the two Finsler spaces has been discussed.


Keywords

Finsler space, hypersurfaces, generalized Kropina conformal change, projective change, fundamental tensors

Keywords


Finsler space, hypersurfaces, generalized Kropina conformal change, projective change, fundamental tensors.

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References


C. Shibata, On invariant tensors of - changes of Finsler metrics, J. Math. Kyoto Univ., 24(1) (1984) 163-188.

H. Rund, The differential geometry of Finsler Spaces, Springer-Verlag, (1959).

M. K. Gupta and P. N. Pandey, On hypersurface of a Finsler space with Randers conformal metric, Tensor N.S., 70(3) (2008) 229-240.

M. K. Gupta and P. N. Pandey, On Hypersurface of a Finsler space with a special metric, Acta. Math. Hungar. 120 (2008) 165-177.

M. K. Gupta and P. N. Pandey, Hypersurfaces of conformally and h-conformally related Finsler space, Acta Math. Hungar., 123(3) (2009) 257-264.

M. K. Gupta, Abhay Singh and P. N. Pandey, On a Hypersurface of a Finsler Space with Randers Change of Matsumoto Metric, Geometry (2013).

Makoto Matsumoto, Projective changes of Finsler metrics and projectively flat Finsler spaces, Tensor N. S., 34 (1980) 303-315.

Makoto Matsumoto, The induced and intrinsic Finsler connections of a hypersurface and Finslerian projective geometry, J. Math. Kyoto Univ., 25(1) (1985) 107-144.

Makoto Matsumoto, Theory of Finsler spaces with (alpha beta)-metric, Reports on Mathematical Physics, 31(1) (1992) 43-83.

M. S. Knebelman, Conformal geometry of generalised metric spaces, Proc. Nat. Acad. Sci., 15 (1929) 376-379.

P. L. Antonelli (ed.), Handbook of Finsler Geometry, Kluwer Academic Publishers, Dordrecht, (2003).

T. Yamada, On Finsler hypersufaces satisfying certain conditions, Tensor N. S., 43 (1986) 56-65.




DOI: https://doi.org/10.22190/FUMI1705763S

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