文献类型：期刊文献

中文题名：A Gauss-Bonnet-Chern theorem for complex Finsler manifolds

英文题名：A Gauss-Bonnet-Chern theorem for complex Finsler manifolds

作者：Zhao Wei[1]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2016

卷号：59

期号：3

起止页码：515

中文期刊名：Science China Mathematics

外文期刊名：SCIENCE CHINA-MATHEMATICS

收录：;Scopus;WOS:【SCI-EXPANDED(收录号:WOS:000369948900008)】；CSCD:【CSCD2015_2016】；PubMed;

基金：This work was supported by TianYuan Foundation of National Natural Science Foundation of China (Grant No. 11426108) and the Fundamental Research Funds for the Central Universities. The author thanks Professor Y. Shen and Professor Z. Shen for their advice and encouragement.

语种：英文

中文关键词：complex Finsler manifold the Gauss-Bonnet-Chern theorem transgression method

外文关键词：complex Finsler manifold; the Gauss-Bonnet-Chern theorem; transgression method

摘要：Using Chern's method of transgression and the currents, we establish a Gauss-Bonnet-Chern theorem for general closed complex Finsler manifolds(M, F). This result extends the classical Gauss-Bonnet-Chern theorem for Hermitian manifolds. Furthermore, a simplified version of the Gauss-Bonnet-Chern theorem is obtained in the case of complex Berwald 1-manifolds.
Using Chern's method of transgression and the currents, we establish a Gauss-Bonnet-Chern theorem for general closed complex Finsler manifolds (M, F). This result extends the classical Gauss-Bonnet-Chern theorem for Hermitian manifolds. Furthermore, a simplified version of the Gauss-Bonnet-Chern theorem is obtained in the case of complex Berwald 1-manifolds.