Bochner-Kodaira techniques on Kähler Finsler manifolds

Abstract

A horizontal Hodge Laplacian operator ▭ _H is defined for Hermitian holomorphic vector bundles over PTM on Kähler Finsler manifold, and the expression of ▭ _H is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler connection. The vanishing theorem is obtained by using the \partial _\mathcal{H} \bar \partial _\mathcal{H} -method on Kähler Finsler manifolds.

Keywords

Kähler Finsler manifold / Horizontal Hodge Laplacian operator, Bochner-Kodaira technique

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