A note on the Gauss-Bonnet-Chern theorem for general connection

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• 作者：Haoran Zhao ; ^{zhaohaoran81@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：58J20
• 刊名：Journal of Geometry and Physics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：98
• 期：Complete
• 页码：414-419
• 全文大小：365 K

文摘

In this paper, we prove a local index theorem for the DeRham Hodge–Laplacian which is defined by the connection compatible with metric. This connection need not be the Levi-Civita connection. When the connection is Levi-Civita connection, this is the classical local Gauss–Bonnet–Chern theorem.