On spherical submanifolds with finite type spherical Gauss map

Bektas B., Dursun U.

ADVANCES IN GEOMETRY, vol.16, no.2, pp.243-251, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1515/advgeom-2016-0005
  • Journal Name: ADVANCES IN GEOMETRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.243-251
  • Istanbul Technical University Affiliated: No

Abstract

Chen and Lue (2007) initiated the study of spherical submanifolds with finite type spherical Gauss map. In this paper, we firstly prove that a submanifold M-n of the unit sphere Sm-1 has non-mass-symmetric 1-type spherical Gauss map if and only if M-n is an open part of a small n-sphere of a totally geodesic (n+1)-sphere Sn+1 subset of Sm-1. Then we show that a non-totally umbilical hypersurface M of Sn+1 with nonzero constant mean curvature in Sn+1 has mass-symmetric 2-type spherical Gauss map if and only if the scalar curvature curvature of M is constant. Finally, we classify constant mean curvature surfaces in S-3 with mass-symmetric 2-type spherical Gauss map.