Abstract

In 1985 Matsumoto [1] discussed the properties of special hypersurface of Rander space with bi(x) being gradient of scalar function b(x). He has considered a hypersuface which is given by b(x)=constant. In 2009 Prasad and Shukla[2] have considered the hypersurface of generalized Matsumoto space with the same equation b(x) = constant. In this paper our study confines to the hypersurface of a Finsler space with special (α,β) metric α cosh β/α + β given by b(x) = constant. We will find out the conditions under which the hypersurface is a hyperplane of first or second kind have been obtained. This hyperplane is not a hyperplane of third kind.

References

[1] M.Matsumoto, The induced and intrinsic connection of a hyperplane and Finslerian projective geometry, J.Math.Kyoto univ, 25(1985) 107-144.
[2] B.N .Prasad, H.S.Shukla and A.P. Tiwari, Hypersurface of a Generalized Matsumoto space, Journal of international academy of physical sciences, vol.13 No.1 (2009) pp-25-38.
[3] M.Matsumoto, on C-reducible Finsler spaces, Tensor, N.S.24 (1972) 29-37.
[4] M.Matsumoto, On Finsler space with Rander metric and special form of important tensors, J.Math.Kyoto Univ., 14(1974)477-498.
[5] C. Shibata, On Finsler space with Kropina metric, Reports on Mathematical physics, 13(1978) 117-128.
[6] G.S.Asanov, C-reducible Finsler spaces. Finsler spaces with Rander metric and Kropina metric, (Russian). Problem of geom.11 (1980), 65-88. English trans. J. sov.Math. 17 (1981) 1610-1624.
[7] C, .Shibata, On Finsler spaces with (α, β) - metric, J. Hokkaido univ of Education, 35 (1) (1984) 1-16.
[8] M. Matsumoto, Theory of Finsler spaces with (α,β) -metric, Rep.on Math, phys. 31(1992), 43-83.

[9] M.Matsumoto, Foundation of Finsler geometry and special Finsler spaces, Kaiseisha Press, Otsu, 520, Japan, (1986).

[10] U.P.Singh and Bindu kumari, on a hypersurface of a Matsumoto space, Indian J. Pure and Appl.Math. 32-4 (2001) 521-531.