Wu's theorem for Kähler-Finsler spaces
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.
scientific article; zbMATH DE number 6419308
scientific article