Rigidity of some Weyl manifolds with nonpositive sectional curvature期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Rigidity of some Weyl manifolds with nonpositive sectional curvature

Authors:	Maciej P Wojtkowski

Institution:	Department of Mathematics, University of Arizona, Tucson, Arizona 85721

Abstract:	We provide a list of all locally metric Weyl connections with nonpositive sectional curvatures on two types of manifolds, -dimensional tori $\mathbb{T}^{n}$ and $\mathbb{M}^{n} =\mathbb{S}^{1}\times \mathbb{S}^{n-1}$ with the standard conformal structures. For $\mathbb{M}^{n}$ we prove that it carries no other Weyl connections with nonpositive sectional curvatures, locally metric or not. In the case of $\mathbb{T}^{n}$ we prove the same in the more narrow class of integrable connections.

Keywords:	Weyl connection nonpositive sectional curvature

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