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Hodge decomposition theorem on strongly Kähler Finsler manifolds

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Abstract

Faran posed an open problem about analysis on complex Finsler spaces: Is there an analogue of the \(\bar \partial \)-Laplacian? Is there an analogue of Hodge theory? Under the assumption that (M, F) is a compact strongly Kähler Finsler manifold, we define a \(\bar \partial \)-Laplacian on the base manifold. Our result shows that the well-known Hodge decomposition theorem in Kähler manifolds is still true in the more general compact strongly Kähler Finsler manifolds.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Zhong Chunping & Zhong Tongde

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310028, China

    Zhong Chunping

Authors
  1. Zhong Chunping
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  2. Zhong Tongde
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Correspondence to Zhong Chunping.

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Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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Zhong, C., Zhong, T. Hodge decomposition theorem on strongly Kähler Finsler manifolds. SCI CHINA SER A 49, 1696–1714 (2006). https://doi.org/10.1007/s11425-006-2055-8

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  • DOI: https://doi.org/10.1007/s11425-006-2055-8

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