Wu's theorem for Kähler-Finsler spaces
type: Item
instance of: scholarly article
title: Wu's theorem for Kähler-Finsler spaces
zbMATH Open document ID: 1317.53100
author: Rongmu Yan
author: Xinxiang Chen
published in: Advances in Mathematics
publication date: 2015-03-25T00:00:00Z
review text: Wu's theorem, Proposition 1.17 in: [\textit{R. E. Greene} and \textit{H. Wu}, Function theory on manifolds which possess a pole. Lecture Notes in Mathematics. 699. Berlin-Heidelberg-New York: Springer-Verlag (1979; Zbl 0414.53043)], attests that the universal covering space of any complete Kähler manifold with nonpositive sectional curvature is always a Stein manifold, (i.e., a closed complex submanifold of some \(\mathbb{C}^N\)). The authors give some generalizations of this theorem in complex Finsler geometry. They prove that a strongly convex Kähler-Berwald manifold with a pole is a Stein manifold if it has nonpositive radial horizontal flag curvature. A similar result is obtained for strongly convex Kähler-Finsler manifolds which possess a complex pole. Finally, a comparison between the horizontal flag curvature and the flag curvature of Riemann-Finsler manifolds is described.
reviewed by: Nicoleta Aldea
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 6419308
zbMATH Keywords: complex Finsler manifold
zbMATH Keywords: flag curvature
zbMATH Keywords: horizontal flag curvature
zbMATH Keywords: Stein manifold
zbMATH Keywords: strongly convex Kähler-Finsler manifold
MaRDI profile type: Publication
full work available at URL: j.aim.2015.02.010
OpenAlex ID: W1973646925
cites work: Finsler metrics - a global approach. With applications to geometric function theory
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cites work: Function theory on manifolds which possess a pole
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cites work: Affinely equivalent Kähler-Finsler metrics on a complex manifold
cites work: Q4517541
DOI: 10.1016/J.AIM.2015.02.010
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description: scientific article; zbMATH DE number 6419308