A vanishing theorem on Kaehler Finsler manifolds

作者：Zhong Chunping^*

来源：Differential Geometry and its Applications, 2009, 27(4): 551-565.

DOI：10.1016/j.difgeo.2009.01.013

• Vanishing theorem
• Kaehler Finsler manifold
• Complex horizontal Laplacian

Let M be a connected compact complex manifold endowed with a strongly pseudoconvex complex Finsler metric F. In this paper, we first define the complex horizontal Laplacian h and complex vertical Laplacian rectangle(v) on the holomorphic tangent bundle T(1.0)M of M, and then we obtain a precise relationship among rectangle(h), rectangle(v), and the Hodge-Laplace operator Delta on (T(1.0)M, <.,.>), where <.,.>) is the induced Hermitian metric on T(1.0)M by F. As an application, we prove a vanishing theorem of holornorphic p-forms on M under the condition that F is a Kaehler Finsler metric on M.

• 出版日期2009-8
• 单位厦门大学