Taiwanese Journal of Mathematics

HYPERSURFACES WITH POINTWISE 1-TYPE GAUSS MAP

Ugur Dursun

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Abstract

In this paper we prove that an oriented hypersurface $M$ of a Euclidean space $E^{n+1}$ has pointwise 1-type Gauss map of the first kind if and only if $M$ has constant mean curvature. Then we conclude that all oriented isoparametric hypersurfaces of $E^{n+1}$ has 1-type Gauss map. We also show that a rational hypersurface of revolution in a Euclidean space $E^{n+1}$ has pointwise 1-type Gauss map of the second kind if and only if it is a right n-cone.

Article information

Source
Taiwanese J. Math., Volume 11, Number 5 (2007), 1407-1416.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404873

Digital Object Identifier
doi:10.11650/twjm/1500404873

Mathematical Reviews number (MathSciNet)
MR2368658

Zentralblatt MATH identifier
1136.53015

Subjects
Primary: 53B25: Local submanifolds [See also 53C40] 53C40: Global submanifolds [See also 53B25]

Keywords
hypersurface of revolution mean curvature finite type Gauss map

Citation

Dursun, Ugur. HYPERSURFACES WITH POINTWISE 1-TYPE GAUSS MAP. Taiwanese J. Math. 11 (2007), no. 5, 1407--1416. doi:10.11650/twjm/1500404873. https://projecteuclid.org/euclid.twjm/1500404873


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