HORIZONTAL LAPLACE OPERATOR IN REAL FINSLER VECTOR BUNDLES  

作　　者：钟春平 钟同德 

机构地区：[1]School of Mathematical Sciences,Xiamen University

出　　处：《Acta Mathematica Scientia》2008年第1期128-140,共13页数学物理学报（B辑英文版）

基　　金：supported by Tian Yuan Foundation of China (10526033);China Postdoctoral Science Foundation (2005038639);the Natural Science Foundation of China (10601040,10571144).

摘　　要：A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.

关 键 词：h-Laplace operator h-harmonic Finsler vector bundle 

分 类 号：O183.1[理学—数学]