Jñānābha‎, Vol. 50 (1) (2020), 49-56

ON HYPERSURFACE OF THE FINSLER SPACE OBTAINED BY CONFORMAL β− CHANGE

By

H. S. Shukla1, Neelam Mishra2 and Vivek Shukla3
1&2
Department of Mathematics & Statistics
DDU Gorakhpur University,Gorakhpur-273009, Uttar Pradesh, India
3
Department of Mathematics, K.D.R.T.P.G. College, Dumari Khas,
Gorakhpur-273202, U.P., India
Email:profhsshuklagkp@rediffmail.com, pneelammishra@gmail.com,
shukladrvivek13@gmail.com (corresponding author)
(Received : February 26, 2020 ; Revised: March 09, 2020)


Abstract

The conformal β− change of Finsler metric L(x, y) is given by L∗(x, y) = eσ(x) f (L(x, y), β(x, y)), where σ(x) is a function of x, β(x, y) = b i (x)yi is a one-form on the underlying manifold Mn , and f(L(x, y), β(x, y)) is a homogeneous function of degree one in L and βLet Fn and F∗n be Finsler spaces with metric functions L and L respectively. In this paper we study the hypersurface of F∗n and find condition under which this hypersurface becomes a hyperplane of first kind, a hyperplane of second kind and a hyperplane of third kind. In this endeavour we connect quantities of F∗n with those of Fn . When the hypersurface of F∗n is a hyperplane of first kind, we investigate the conditions under which it becomes a Landsberg space, a Berwald space, or a locally Minkowskian space.

2010 Mathematics Subject Classifications: 53B40, 53C60.
Keywords and phrases: Finsler space, Hypersurface, Cartan-parallel, Hyperplane, Confor-mal β−change, Homothetic β−change.