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.
