A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the ...A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.展开更多
Let （E, F） be a complex Finsler vector bundle over a compact Kahler manifold （M, g） with Kahler form φ We prove that if （E, F） is a weakly complex Einstein-Finsler vector bundle in the sense of Aikou （1997）, ...Let （E, F） be a complex Finsler vector bundle over a compact Kahler manifold （M, g） with Kahler 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 Kahler manifold （M, g） is necessarily φ-semistable and （E,F）=（E1,F1）……（Ek,Fk）,where Fj ：= F｜Ej, and each （Ej, Fj） 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）.展开更多
Let(M,g)be a compact Kihler manifold and(E,F)be a holomorphic Finsler vector bundle of rank r≥2 over M.In this paper,we prove that there exists a Kahler metricФdefined on the projective bundle P(E)of E,which comes n...Let(M,g)be a compact Kihler manifold and(E,F)be a holomorphic Finsler vector bundle of rank r≥2 over M.In this paper,we prove that there exists a Kahler metricФdefined on the projective bundle P(E)of E,which comes naturally from g and F.Moreover,a necessary and sufficient condition forФhaving positive scalar curvature is obtained,and a sufficient condition forФhaving positive Ricci curvature is established.展开更多
基金supported by Tian Yuan Foundation of China (10526033)China Postdoctoral Science Foundation (2005038639)the Natural Science Foundation of China (10601040,10571144).
文摘A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.
基金supported by National Natural Science Foundation of China(Grant Nos.11671330 and 11271304)the Fujian Province Natural Science Funds for Distinguished Young Scholar(Grant No.2013J06001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Let （E, F） be a complex Finsler vector bundle over a compact Kahler manifold （M, g） with Kahler 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 Kahler manifold （M, g） is necessarily φ-semistable and （E,F）=（E1,F1）……（Ek,Fk）,where Fj ：= F｜Ej, and each （Ej, Fj） 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）.
基金the National Natural Science Foundation of China(Grant No.11671330)。
文摘Let(M,g)be a compact Kihler manifold and(E,F)be a holomorphic Finsler vector bundle of rank r≥2 over M.In this paper,we prove that there exists a Kahler metricФdefined on the projective bundle P(E)of E,which comes naturally from g and F.Moreover,a necessary and sufficient condition forФhaving positive scalar curvature is obtained,and a sufficient condition forФhaving positive Ricci curvature is established.
