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| BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS | |
| 引用本文： | 钟同德,钟春平. BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS[J]. 数学物理学报(B辑英文版), 2003, 23(2) |
| 作者姓名： | 钟同德 钟春平 |
| 作者单位： | Institute of Mathematics，Xiamen University，Institute of Mathematics，Xiamen University Xiamen 361005，China，Xiamen 361005，China |
| 基金项目： | Project supported by the Natural Science Foundation of China(10271097) |
| 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 A 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. |
BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS |
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| Zhong Tongde Zhong ChunpingInstitute of Mathematics,Xiamen University,Xiamen ,China. BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS[J]. Acta Mathematica Scientia, 2003, 23(2) | |
| Authors: | Zhong Tongde Zhong ChunpingInstitute of Mathematics Xiamen University Xiamen China |
| Affiliation: | Zhong Tongde Zhong ChunpingInstitute of Mathematics,Xiamen University,Xiamen 361005,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 A 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. |
| Keywords: | Finsler manifold Laplace operator killing vector field harmonic 1-form Bochner type vanishing theorem |
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