On spherical submanifolds with finite type spherical Gauss map

Yükleniyor...
Küçük Resim

Tarih

2016-04-01

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Walter De Gruyter GMBH

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Araştırma projeleri

Organizasyon Birimleri

Dergi sayısı

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 Mn of the unit sphere double-struck Sm-1 has non-mass-symmetric 1-type spherical Gauss map if and only if Mn is an open part of a small n-sphere of a totally geodesic (n + 1)-sphere double-struck Sn+1 ? double-struck Sm-1. Then we show that a non-totally umbilical hypersurface M of double-struck Sn+1 with nonzero constant mean curvature in double-struck 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 double-struck S3 with mass-symmetric 2-type spherical Gauss map.

Açıklama

Anahtar Kelimeler

Finite type map, Isoparametric hypersurface, Mean curvature, Spherical Gauss map

Kaynak

Advances in Geometry

WoS Q Değeri

Q4

Scopus Q Değeri

Q3

Cilt

16

Sayı

2

Künye

Bektas, B., & Dursun, U. (2016). On spherical submanifolds with finite type spherical gauss map. Advances in Geometry, 16(2), 243-251. doi:10.1515/advgeom-2016-0005