Positivities and vanishing theorems on complex Finsler manifolds |
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| Affiliation: | 1. School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai, 519000, PR China;2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, PR China;3. Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, PR China |
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| Abstract: | In this paper, we study the relations between curvatures and geometries of a compact complex Finsler manifold. We first introduce various definitions of curvatures and then vanishing theorems are established under some positivity assumptions of curvatures. In particular, we get some criteria of a compact complex Finsler manifold to be of negative Kodaira dimension. |
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| Keywords: | Partial connection Finsler manifolds Laplace operator Vanishing theorem |
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