数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (2): 165-.

• 论文 • 上一篇    下一篇

BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS

 钟同德, 钟春平   

  1. Institute of Mathematics, Xiamen University, Xiamen 361005, China
  • 出版日期:2003-04-07 发布日期:2003-04-07
  • 基金资助:

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

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

摘要:

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.

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

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

中图分类号: 

  • 53C60