Laplacians on the holomorphic tangent bundle of a Kaehler manifold  

作　　者：ZHONG ChunPing School of Mathematical Sciences,Xiamen University,Xiamen 361005,China 

出　　处：《Science China Mathematics》2009年第12期2841-2854,共14页中国科学：数学（英文版）

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)

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.

关 键 词：Kaehler manifold complex horizontal Laplacian vanishing theorem 32Q15 32L20 

分 类 号：O186.1[理学—数学]