| Hodge decomposition theorem on strongly Kahler Finsler manifolds Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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| 作者姓名： | ZHONG Chunping & ZHONG Tongde School of Mathematical Sciences Xiamen University Xiamen China |
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| 作者单位： | ZHONG Chunping & ZHONG Tongde School of Mathematical Sciences，Xiamen University，Xiamen 361005，China; Department of Mathematics，Zhejiang University，Hangzhou 310028，China |
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| 摘 要： | Faran posed an open problem about analysis on complex Finsler spaces: Is there an analogue of the (?)-Laplacian? Is there an analogue of Hodge theory? Under the assumption that (M,F) is a compact strongly Kahler Finsler manifold, we define a (?)-Laplacian on the base manifold. Our result shows that the well-known Hodge decomposition theorem in Kahler manifolds is still true in the more general compact strongly Kahler Finsler manifolds.
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Hodge decomposition theorem on strongly Kahler Finsler manifolds Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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| ZHONG Chunping & ZHONG Tongde School of Mathematical Sciences,Xiamen University,Xiamen ,China,.Hodge decomposition theorem on strongly Kahler Finsler manifolds Dedicated to Professor Sheng GONG on the occasion of his 75th birthday[J].Science in China(Mathematics),2006(11). |
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| Authors: | ZHONG Chunping & ZHONG Tongde School of Mathematical Sciences Xiamen University Xiamen China |
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| Institution: | ZHONG Chunping & ZHONG Tongde School of Mathematical Sciences,Xiamen University,Xiamen 361005,China, Department of Mathematics,Zhejiang University,Hangzhou 310028,China |
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| Abstract: | Faran posed an open problem about analysis on complex Finsler spaces: Is there an analogue of the (?)-Laplacian? Is there an analogue of Hodge theory? Under the assumption that (M,F) is a compact strongly Kahler Finsler manifold, we define a (?)-Laplacian on the base manifold. Our result shows that the well-known Hodge decomposition theorem in Kahler manifolds is still true in the more general compact strongly Kahler Finsler manifolds. |
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| Keywords: | strongly Kahler Finsler Hodge decomposition theorem (?)-Laplacian |
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