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Slant Vector Fields on the Hypersurfaces

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Abstract

In the present paper, we introduce the concept of a slant vector field \(\chi\) 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 \(\chi\), say \(\alpha\), defined on an open interval I containing 0 such that \(\alpha (0)=p\), 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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Authors and Affiliations

  1. Department of Mathematics, Tafresh University, Tafresh, 39518-79611, Iran

    Parsian Ali

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  1. Parsian Ali
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Correspondence to Parsian Ali.

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Parsian, A. Slant Vector Fields on the Hypersurfaces. Iran J Sci Technol Trans Sci 43, 1191–1195 (2019). https://doi.org/10.1007/s40995-018-0580-2

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  • DOI: https://doi.org/10.1007/s40995-018-0580-2

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