On spherical submanifolds with finite type spherical Gauss map

Bektas B., Dursun U.

ADVANCES IN GEOMETRY, cilt.16, sa.2, ss.243-251, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1515/advgeom-2016-0005
  • Dergi Adı: ADVANCES IN GEOMETRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.243-251
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

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.