Scalar curvature of Lie groups

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Feb 1981 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 81, pages 311-315 (issn: 0002-9939, eissn: 1088-6826,

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Authors: Lai, Heng-Lung; Lue, Huei-Shyong;

doi: 10.1090/s0002-9939-1981-0593479-4 , 10.2307/2044216

Scalar curvature of Lie groups

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Abstract

In this paper, we prove the following theorem: If G G is a connected Lie group, then G G admits left invariant metric of positive scalar curvature if and only if the universal covering space G ~ \tilde G of G G is not homeomorphic to the Euclidean space.

Keywords

flat, Differential geometry of homogeneous manifolds, left invariant metric, General properties and structure of real Lie groups, scalar curvature, universal covering group

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