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Laplacian on Complex Finsler Manifolds

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Chinese Annals of Mathematics,Series B 2011年第4期32卷 507-520页

作者： Jinxiu XIA tongde zhong chunhui qiu Department of Applied Mathematics Tongji University Shanghai 200092 China. school of mathematical sciences Xiamen University Xiamen 361005 Fujian China.

In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M, F ). Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle T 1,0 M is obtained.

关键词： Laplacian Strongly pseudoconvex complex Finsler metric Chern Finsler connection

Bochner-Kodaira Techniques on Kahler Finsler Manifolds

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Chinese Annals of Mathematics,Series B 2015年第1期36卷 125-140页

作者： Jinxiu XIAO chunhui qiu tongde zhong school of Advanced Vocational Education Shanghai University of Engineering Science school of mathematical sciences Xiamen University

A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler *** vanishing theorem is obtained by using the α_Hα_H-method on Kahler Finsler manifolds.

关键词： Kahler Finsler manifold Horizontal Hodge Laplacian operator Bochner-Kodaira technique

Integral formulas for differential forms of type (p,q) on complex Finsler manifolds

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Science china Mathematics 2004年第2期47卷 284-296页

作者： qiu chunhui zhong tongde Department of Mathematics Xiamen University Xiamen 361005 China Department of Mathematics Xiamen University Xiamen 361005 China

Using the invariant integral kernel introduced by Demailly and Laurent-Thiebaut, complex Finsler metric and nonlinear connection associating with Chern-Finsler connection, we research the integral representation theory on complex Finsler manifolds. The Koppelman and Koppelman-Leray formulas are obtained, and the $\overline \partial $-equations are solved.

关键词： complex Finsler manifold Chern-Finsler connection invariant integral kernel Koppelman-Leray formula $$\overline \partial $$ -equation

On conformal complex Finsler metrics

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Science china Mathematics 2022年第7期65卷 1517-1530页

作者： Hongjun Li chunhui qiu Hongchuan Xia Guozhu zhong school of Mathematics and Statistics Henan UniversityKaifeng 475004China school of mathematical sciences Xiamen UniversityXiamen 361005China school of Mathematics and Statistics Xinyang Normal UniversityXinyang 464000China

In this paper,we study conformal transformations in complex Finsler *** first prove that two weakly Kahler Finsler metrics cannot be ***,we give a necessary and sufficient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal weakly Kahler ***,we discuss conformal transformations of a strongly pseudoconvex complex Finsler metric,which preserve the geodesics,holomorphic S-curvatures and mean Landsberg tensors.

关键词： weakly Kahler Finsler metric locally conformal weakly Kahler Finsler metric geodesic holomorphic S-curvature mean Landsberg tensor