Totally geodesic shadow boundary submanifolds and a characterization for {mathbb{S}}^n期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Totally geodesic shadow boundary submanifolds and a characterization for {mathbb{S}}^n

Authors:	Gabriel Ruiz-Hernández

Affiliation:	(1) CIMAT, Jalisco s.n., Mineral de Valenciana Guanajuato, 36240, México

Abstract:	We prove that the sphere ${mathbb{S}}^n$ is the only compact immersed hypersurface in Euclidean space ${mathbb{R}}^{n+1}$ each of whose shadow boundaries is a totally geodesic submanifold. Furthermore, we give conditions for the shadow boundary of a submanifold of ${mathbb{R}}^{n+1}$ to be regular. Received: 25 January 2007

Keywords:	53A07
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