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.
基金
Tian Yuan Foundation of National Natural Science Foundation of China (Grant No. 11426108)
the Fundamental Research Funds for the Central Universities
