Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (2): 165-.

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BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS

 ZHONG Tong-De, ZHONG Chun-Beng   

  1. Institute of Mathematics, Xiamen University, Xiamen 361005, China
  • Online:2003-04-07 Published:2003-04-07
  • Supported by:

    Received October 8,2000. Project supported by the Natural Science Foundation of China

Abstract:

Using non-linear connection of Finsler manifold M, the existence of local
coordinates which is normalized at a point x is proved, and the Laplace operator △ on
1-form of M is defined by non-linear connection and its curvature tensor. After proving the
maximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theorem
of Killing vectors and harmonic 1-form are obtained.

Key words: Finsler manifold, Laplace operator, killing vector field, harmonic 1-form, Bochner type vanishing theorem

CLC Number: 

  • 53C60
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