Horizontal Connection and Horizontal Mean Curvature in Carnot Groups

作     者：Kang Hai TAN Xiao Ping YANG 

作者机构：Department of Applied MathematicsNanjing University of Science and Technology 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2006年第22卷第3期

页      面：701-710页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(No.10471063) 

主　　题：Carnot groups Nonholonomic connection Horizontal mean curvature Sub-Riemannian minimal surfaces 

摘      要：In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.