Hypersurfaces with pointwise 1-type Gauss map

Dursun U.

TAIWANESE JOURNAL OF MATHEMATICS, cilt.11, sa.5, ss.1407-1416, 2007 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 5
  • Basım Tarihi: 2007
  • Doi Numarası: 10.11650/twjm/1500404873
  • Dergi Adı: TAIWANESE JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1407-1416
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

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.