Hodge theorem for the natural projection of complex horizontal Laplacian on complex Finsler manifolds

DOI10.1016/J.DIFGEO.2014.01.012zbMath1325.53098OpenAlexW2050976386WikidataQ115356358 ScholiaQ115356358MaRDI QIDQ499514

Tongde Zhong, Chunhui Qiu, Jinling Li

Publication date: 30 September 2015

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2014.01.012

zbMATH Keywords

complex Finsler manifoldHodge theoremcomplex horizontal Laplacian

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Global submanifolds (53C40) Hodge theory in global analysis (58A14) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (4)

Hodge and vanishing theorems on complex Finsler vector bundles ⋮ A Laplace operator on complex Finsler manifolds ⋮ Laplacians for the holomorphic tangent bundles with g-nature metrics on complex Finsler manifolds ⋮ Positivities and vanishing theorems on complex Finsler manifolds

Cites Work

• Bochner technique on strong Kähler-Finsler manifolds
• Laplacian on complex Finsler manifolds
• A vanishing theorem on Kähler Finsler manifolds
• Hodge decomposition theorem on strongly Kähler Finsler manifolds
• Kähler Finsler metrics are actually strongly Kähler
• 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
• The Koppelman-Leray formula on complex Finsler manifolds
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