Hodge decomposition theorem on strongly Kahler Finsler manifolds Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

作     者：ZHONG Chunping & ZHONG Tongde School of Mathematical Sciences, Xiamen University, Xiamen 361005, China Department of Mathematics, Zhejiang University, Hangzhou 310028, China 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2006年第11期

页      面：1696-1714页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：strongly Kahler Finsler Hodge decomposition theorem (?)-Laplacian. 

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.