数学物理学报(英文版)

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HORIZONTAL LAPLACE OPERATOR IN REAL FINSLER VECTOR BUNDLES

钟春平; 钟同德   

  1. 厦门大学数学学院, 厦门 361005
  • 收稿日期:2005-12-11 修回日期:1900-01-01 出版日期:2008-01-20 发布日期:2008-01-20
  • 通讯作者: 钟春平
  • 基金资助:

    This work was supported by Tian Yuan Foundation of China (10526033), China Postdoctoral Science Foundation (2005038639), and the Natural Science Foundation of China (10601040, 10571144).

HORIZONTAL LAPLACE OPERATOR IN REAL FINSLER VECTOR BUNDLES

Zhong Chunping; Zhong Tongde   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2005-12-11 Revised:1900-01-01 Online:2008-01-20 Published:2008-01-20
  • Contact: Zhong Chunping

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 h-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

Abstract:

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 h-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.

Key words: h-Laplace operator, h-harmonic, Finsler vector bundle

中图分类号: 

  • 53C60