Finsler流形上取值于向量丛的调和形式

通过定义Finsler流形上取值于向量丛p-形式的整体内积和射影球丛纤维上的积分,得到相应的余微分算子.进而定义Finsler流形上取值于向量丛p-形式的Laplace算子,并证明它是自共轭的椭圆算子.最后证明当目标流形是黎曼流形时,调和映射和取值于拉回切丛的调和1-形式之间的等价关系.

Harmonic Forms with Values in the Vector Bundle over Finsler Manifolds

By defining the global inner product of p-forms with values in the vector bundle over a Finsler manifold and the integral on fibers of a projective sphere bundle,the corresponding codifferential operator is obtained.Then we define the Laplace operator of p-forms valued in the vector bundle over a Finsler manifold and prove that it is elliptic and self-conjugate.Particularly,when the target manifold is Rie mannian,the equivalence between a harmonic map and a harmonic 1-form with values in the pull back tangent bundle is derived.