Homogeneous Riemannian manifolds of positive Ricci curvature |
| |
Authors: | V. N. Berestovskii |
| |
Affiliation: | (1) Omsk State University, USSR |
| |
Abstract: | We prove that a homogeneous effective spaceM=G/H, whereG is a connected Lie group andH⊂G is a compact subgroup, admits aG-invariant Riemannian metric of positive Ricci curvature if and only if the spaceM is compact and its fundamental group π1(M) is finite (in this case any normal metric onG/H is suitable). This is equivalent to the following conditions: the groupG is compact and the largest semisimple subgroupLG⊂G is transitive onG/H. Furthermore, ifG is nonsemisimple, then there exists aG-invariant fibration ofM over an effective homogeneous space of a compact semisimple Lie group with the torus as the fiber. Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 334–340, September, 1995. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|