Hodge decomposition theorem on strongly Kähler Finsler manifolds

DOI10.1007/s11425-006-2055-8zbMath1107.53049OpenAlexW1584946276MaRDI QIDQ867805

Tongde Zhong, Chun-Ping Zhong

Publication date: 16 February 2007

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-006-2055-8

zbMATH Keywords

Hodge decomposition theoremstrongly Kähler Finsler

Mathematics Subject Classification ID

Hodge theory in global analysis (58A14) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items

A vanishing theorem on Kähler Finsler manifolds ⋮ Kähler Finsler metrics and conformal deformations ⋮ Some results on strong Randers metrics ⋮ Hodge and vanishing theorems on complex Finsler vector bundles ⋮ A Laplace operator on complex Finsler manifolds ⋮ On a class of smooth complex Finsler metrics ⋮ Connections on the total space of a holomorphic Lie algebroid ⋮ Characterizations of complex Finsler metrics ⋮ Laplacians for the holomorphic tangent bundles with g-nature metrics on complex Finsler manifolds ⋮ Positivities and vanishing theorems on complex Finsler manifolds ⋮ Hodge theorem for the natural projection of complex horizontal Laplacian on complex Finsler manifolds ⋮ Comparison theorems and their applications on Kähler Finsler manifolds ⋮ Vanishing theorems on holomorphic Lie algebroids ⋮ Holomorphic curvature of complex Finsler submanifolds ⋮ Bochner-Kodaira techniques on Kähler Finsler manifolds ⋮ Laplacian on complex Finsler manifolds ⋮ Kähler Finsler metrics are actually strongly Kähler

Cites Work

• Eigenvalues of second order differential operators on a Finsler manifold
• Finsler metrics - a global approach. With applications to geometric function theory
• Complex spaces in Finsler, Lagrange and Hamilton geometries.
• Horizontal \(\overline\partial\)-Laplacian on complex Finsler manifolds
• Negative Vector Bundles and Complex Finsler Structures
• Generalized Metrics on Complex Manifolds
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