H. S. Shukla^{1}, Neelam Mishra^{2} and Vivek Shukla^{3}1&2Department of Mathematics & StatisticsDDU Gorakhpur University,Gorakhpur-273009, Uttar Pradesh, India3Department of Mathematics, K.D.R.T.P.G. College, Dumari Khas,Gorakhpur-273202, U.P., IndiaEmail:profhsshuklagkp@rediffmail.com, pneelammishra@gmail.com,shukladrvivek13@gmail.com (corresponding author)(Received : February 26, 2020 ; Revised: March 09, 2020)AbstractThe conformal β− change of Finsler metric L(x, y) is given by L∗(x, y) = e^{σ(x)} f (L(x, y), β(x, y)), where σ(x) is a function of x, β(x, y) = b i (x)y^{i} is a one-form on the underlying manifold M , and ^{n}f(L(x, y), β(x, y)) is a homogeneous function of degree one in L and β. Let F and ^{n}F be Finsler spaces with metric functions ^{∗n}L and L respectively. In this paper we study the hypersurface of ^{∗}F 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 ^{∗n}F with those of ^{∗n}F . When the hypersurface of ^{n}F 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.^{∗n}2010 Mathematics Subject Classifications: 53B40, 53C60.Keywords and phrases: Finsler space, Hypersurface, Cartan-parallel, Hyperplane, Confor-mal β−change, Homothetic β−change. |

Jñānābha > Volume 50 (No 1-2020) >