Acta mathematica scientia, Series B >
BOCHNER TECHNIQUE ON STRONG KÄHLER-FINSLER MANIFOLDS
Received date: 2008-04-24
Online published: 2010-01-20
Supported by
Supported by the National Natural Science Foundation of China (10571144, 10771174) and Program for New Centery Excellent Talents in Xiamen University.
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=T1,0M \ 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.
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 . DOI: 10.1016/S0252-9602(10)60025-2
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