Hypersurfaces with pointwise 1-type Gauss map

Dursun U.

TAIWANESE JOURNAL OF MATHEMATICS, vol.11, no.5, pp.1407-1416, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 5
  • Publication Date: 2007
  • Doi Number: 10.11650/twjm/1500404873
  • Journal Name: TAIWANESE JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1407-1416
  • Istanbul Technical University Affiliated: No

Abstract

In this paper we prove that an oriented hypersurface M of a Euclidean space En+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 En+1 has 1-type Gauss map. We also show that a rational hypersurface of revolution in a Euclidean space En+1 has pointwise 1-type Gauss map of the second kind if and only if it is a right n-cone.