BOCHNER TECHNIQUE ON STRONG KÄHLER-FINSLER MANIFOLDS

doi:10.1016/S0252-9602(10)60025-2

Abstract

Abstract:

By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong Kähler-Finsler manifolds is studied. For a strong Kähler-Finsler manifold M, the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈M=T^1,0M \ o(M), and then the horizontal Laplace operator ΟH for differential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor, and the horizontal Laplace operator ?H on holomorphic vector bundle over PTM is also defined. Finally, we get a Bochner vanishing theorem for differential forms on PTM. Moreover, the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained.

Key words: Bochner technique, strong Kähler-Finsler manifold, horizontal Hodge-Laplace operator, Weitzenböck formula

CLC Number:

32Q15

XIAO Jin-Xiu, ZHONG Tong-De, QIU Chun-Hui. BOCHNER TECHNIQUE ON STRONG KÄHLER-FINSLER MANIFOLDS[J].Acta mathematica scientia,Series B, 2010, 30(1): 89-106.

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