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On the steinness of strongly convex Kähler Finsler manifolds. (English) Zbl 1478.32030

Summary: In this paper, we study Steinness of nonpositively or nonnegatively curved strongly convex Kähler Finsler manifolds. In particular, we prove that every strongly convex Kähler Finsler manifold with a pole and nonpositive bisectional curvature must be Stein. In addition, every complete noncompact and strongly convex Kähler Berwald manifold is Stein if it has positive flag curvature everywhere, or it has nonnegative flag curvature and everywhere positive holomorphic bisectional curvature.

MSC:

32E10 Stein spaces
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
32Q15 Kähler manifolds
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