Slant Vector Fields on the Hypersurfaces (original) (raw)

Iranian Journal of Science and Technology, Transactions A: Science

Abstract

In the present paper, we introduce the concept of a slant vector field \chi$$χ defined on a hypersurface S, as a generalization of the tangent vector field on S, and investigate the problem of its existence, uniqueness and integral curve. Among other things, we provide an integral equation and also a differential equation for the integral curve of \chi$$χ, say \alpha$$α, defined on an open interval I containing 0 such that \alpha (0)=p$$α(0)=p, where p is an arbitrary point of the hypersurface. At the end, we also investigate some special cases and some examples.

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