Let (M,g) be a compact Kahler manifold and (E,F) be a holomorphic Finsler vector bundle of rank r ≥ 2over M. In this paper, we prove that there exists a Kähler metric Φ defined on the projective bundle P(E)of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for Φ having positive scalar curvature is obtained, and a sufficient condition for Φ having positive Ricci curvature is established.

中文翻译：

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全纯Finsler向量束的投射束上的Kähler度量

令（M，G）是紧凑卡勒歧管和（E，F）是秩的全纯芬斯拉向量丛ř ≥2over中号。在本文中，我们证明了存在一个凯勒度量Φ上的投影束定义P（Ë的）ë，它从顺其自然克和˚F。此外，对于一个充分必要条件Φ得到具有正标量曲率，并且对于充分条件Φ建立具有正曲率。