强K(a)hler-Finsler流形上(p,q)形式的中值Laplace算子

本文给出了强K(a)hler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等.与K(a)hler流形上利用逆变基本张量11]及其在Finsler流形上的变形5,10]作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强K(a)hler-Finsler流形上的逆变密切Kahler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强K(a)hler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广.

Mean-Value Laplacian for(p,q)-forms on Strongly K(a)hler-Finsler Manifolds

Some properties of the mean-value Laplacian for functions of strongly K(a)hler-Finsler manifolds such as self-adjointness and the divergence form are given. Differ from the classical case as in K(a)hler manifold using contravariant fundamental tensor11] and using its variance in Finsler manifold5,10] as density to define the pointwise and global inner product, the authors using contravariant osculating K(a)hler metric as density to define the pointwise and global inner product, and then define the Hodge-Laplace operator for strongly K(a)hler-Finsler manifolds, which may be regarded as the extension of mean-value Laplacian for functions.