Displaying similar documents to “Holomorphic curvature of infinite dimensional symmetric complex Banach manifolds of compact type.”

Some results on curvature and topology of Finsler manifolds

Bing Ye Wu (2013)

Annales Polonici Mathematici

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We investigate the curvature and topology of Finsler manifolds, mainly the growth of the fundamental group. By choosing a new counting function for the fundamental group that does not rely on the generators, we are able to discuss the topic in a more general case, namely, we do not demand that the manifold is compact or the fundamental group is finitely generated. Among other things, we prove that the fundamental group of a forward complete and noncompact Finsler n-manifold (M,F) with...

On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach

Csaba Vincze, Tahere Reza Khoshdani, Sareh Mehdi Zadeh Gilani, Márk Oláh (2019)

Communications in Mathematics

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In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.

Stable harmonic maps between Finsler manifolds and Riemannian manifolds with positive Ricci curvature

Jintang Li (2010)

Annales Polonici Mathematici

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We study the stability of harmonic maps between Finsler manifolds and Riemannian manifolds with positive Ricci curvature, and we prove that if Mⁿ is a compact Einstein Riemannian minimal submanifold of a Riemannian unit sphere with Ricci curvature satisfying R i c M > n / 2 , then there is no non-degenerate stable harmonic map between M and any compact Finsler manifold.

Some rigidity theorems for Finsler manifolds of sectional flag curvature

Bing Ye Wu (2010)

Archivum Mathematicum

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In this paper we study some rigidity properties for Finsler manifolds of sectional flag curvature. We prove that any Landsberg manifold of non-zero sectional flag curvature and any closed Finsler manifold of negative sectional flag curvature must be Riemannian.