Acta mathematica scientia,Series B

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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

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

CLC Number: 

  • 53C60
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