A PARTIAL CONNECTION ON COMPLEX FINSLER BUNDLES AND ITS APPLICATIONS

摘要

Let π: E → M be a holomorphic vector bundle over a complex manifold M, and p: PE → M the projective bundle of E. If a complex Finsler structure F is given on E, a natural Hermitian structure H on the pull-back E = p~(-1) E is defined, and the differential geometry of (E, H) has been studied (cf. Abate-Patrizio, Aikou, Faran, Kobayashi, Royden). In particular, Kobayashi gave a differential geometric characterization of negative holomorphic vector bundles, and proved a vanishing theorem for holomorphic sections of a complex Finsler bundle.