Weakly complex Einstein-Finsler vector bundle |
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Authors: | Liling Sun Chunping Zhong |
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Institution: | 1.College of Mathematics,Taiyuan University of Technology,Taiyuan,China;2.School of Mathematical Sciences,Xiamen University,Xiamen,China |
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Abstract: | Let (E, F) be a complex Finsler vector bundle over a compact Kähler manifold (M, g) with Kähler form Φ. We prove that if (E, F) is a weakly complex Einstein-Finsler vector bundle in the sense of Aikou (1997), then it is modeled on a complex Minkowski space. Consequently, a complex Einstein-Finsler vector bundle (E, F) over a compact Kähler manifold (M, g) is necessarily Φ-semistable and (E, F) = (E1, F1) ? · · · ? (Ek; Fk); where F j := F |E j , and each (E j , F j ) is modeled on a complex Minkowski space whose associated Hermitian vector bundle is a Φ-stable Einstein-Hermitian vector bundle with the same factor c as (E, F). |
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