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On the Hypersurface of a Finsler Space with the Special Metric βn+1 α+ (α−β)n

Authors

Gauree Shanker, G. C. Chaubey and Vinay Pandey

Abstract

In the present paper, we consider a n−dimentional Finsler space F^n = (M^n , L) with (α, β)−metric L(α, β) = α + β^n+1/ (α−β)^n which is a generalization of the metric α + β^2/(α−β) considered in [9] and the hypersurface of F n with b_i(x) = ∂_i b being the gradient of a scalar function b(x). We find the conditions for this
hypersurface to be a hyperplane of 1st kind, 2nd kind and we also show that
this hypersurface is a hyperplane of 3rd kind if and only if it is a hyperplane of
first kind

Keywords and Phrases : Hypersurface, Hyperplane, (α, β)-metric, Normal
curvature vector, Second fundamental tensor.
AMS Subject Classification : : 53B40, 53C60

Received date : January 14, 2013

Accepted date: March 22, 2013

cited by: J.T.S. Vol. 7 (2013), pp.39-47

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