Laplacian on complex Finsler manifolds

Abstract

National Natural Science Foundation of China [10871145, 10771174]; Doctoral Program Foundation of the Ministry of Education of China [2009007Q110053]In this paper, the Laplacian on the holomorphic tangent bundle T (1,0) M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M, F). Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle T (1,0) M is obtained