Affine Connections and Gauss-Bonnet Theorems in the Heisenberg Group  

Heisenberg群上的仿射联络和Gauss-Bonnet定理

作　　者：WANG Yong 王勇(东北师范大学数学与统计学院,吉林长春130024)

机构地区：[1]School of Mathematics and Statistics,Northeast Normal University,Changchun,Jilin,130024,P.R.China

出　　处：《数学进展》2024年第5期1103-1119,共17页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11771070).

摘　　要：In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.本文计算了Heisenberg群中远离示性点的欧几里得C²光滑曲面对应于两种Schou-ten-VanKampen仿射联络和容许联络的高斯曲率的次黎曼极限,以及曲面上欧几里得C2光滑曲线的对应于两种Schouten-VanKampen仿射联络和容许联络的符号测地曲率,得到了Heisen-berg群中对应于两种Schouten-VanKampen仿射联络和容许联络的Gauss-Bonnet定理.

关 键 词：Schouten-Van Kampen affine connection the adapted connection Gauss-Bonnet theorem sub-Riemannian limit Heisenberg group 

分 类 号：O186.1[理学—数学]