Sufficient conditions for one domain to contain another in a space of constant curvature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

Sufficient conditions for one domain to contain another in a space of constant curvature

Authors:	Jiazu Zhou

Affiliation:	Department of Mathematics, Sultan Qaboos University, P.O.Box 36, Al-Khod 123, Sultanate of Oman

Abstract:	As an application of the analogue of C-S. Chen's kinematic formula in the 3-dimensional space of constant curvature , that is, Euclidean space ${mathbb{R}}^{3}$ , -sphere $S^{3}$ , hyperbolic space ${mathbb{H}}^{3}$ (, respectively), we obtain sufficient conditions for one domain to contain another domain in either an Euclidean space $mathbb{R}^{3}$ , or a -sphere $S^{3}$ or a hyperbolic space $mathbb{H}^{3}$ .

Keywords:	Kinematic formula transfer principle Weingarden transformation Gaussian curvature convex body domain mean curvature total geodesic curvature.

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