By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-Finsler manifold M, the authors first prove that there exist...By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-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 NH 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展开更多
Let(M,g_(0))be a compact Riemannian manifold-with-boundary.We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M,via a variational approach a la Kozono-Yanag...Let(M,g_(0))be a compact Riemannian manifold-with-boundary.We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M,via a variational approach a la Kozono-Yanagisawa[Lr-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains,Indiana Univ.Math.J.58(2009),1853-1920],combined with global computations based on the Bochner technique.展开更多
基金Supported by the National Natural Science Foundation of China (10571144,10771174)Program for New Centery Excellent Talents in Xiamen University
文摘By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-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 NH 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
文摘Let(M,g_(0))be a compact Riemannian manifold-with-boundary.We present a new proof of the classical Gaffney inequality for differential forms in boundary value spaces over M,via a variational approach a la Kozono-Yanagisawa[Lr-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains,Indiana Univ.Math.J.58(2009),1853-1920],combined with global computations based on the Bochner technique.
