Finsler流形上取值于向量丛的调和形式

Harmonic Forms with Values in the Vector Bundle over Finsler Manifolds

摘要:

文主要研究Finsler流形上取值于向量丛的p-形式，通过定义其上的整体内积得到相应的余微分算子和Laplace算子，进而证明了调和映射与调和$1$-形式的等价关系.

Abstract:

This paper is mainly to study the p-forms with values in the vector bundle over a Finsler manifold. By defining the global inner product of p-forms,the codifferential operator and the Laplace operator are given. Then the equivalence between harmonic maps and harmonic 1-forms is derived