摘要
Let M be a connected complex manifold endowed with a Hermitian metric g.In this paper,the complex horizontal and vertical Laplacians associated with the induced Hermitian metric <·,·>on the holomorphic tangent bundle T 1,0M of M are defined,and their explicit expressions are obtained.Using the complex horizontal and vertical Laplacians associated with the Hermitian metric <·,·>on T 1,0M,we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T 1,0M under the condition that g is a Kaehler metric on M.
Let M be a connected complex manifold endowed with a Hermitian metric g. In this paper, the complex horizontal and vertical Laplacians associated with the induced Hermitian metric 〈·, ·〉 on the holomorphic tangent bundle T 1,0 M of M are defined, and their explicit expressions are obtained. Using the complex horizontal and vertical Laplacians associated with the Hermitian metric 〈·, ·〉 on T 1,0 M, we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T 1,0 M under the condition that g is a Kaehler metric on M.
基金
supported by the Program for New Century Excellent Talents in Fujian Province and National Natural Science Foundation of China(Grant Nos.10601040,10971170)
