Cohomogeneity Two Riemannian Manifolds of Non-Positive Curvature

Mirzaie, Reza

doi:10.7546/giq-13-2012-233-244

VOL. 13 | 2012 Cohomogeneity Two Riemannian Manifolds of Non-Positive Curvature

Reza Mirzaie

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

Geom. Integrability & Quantization, 2012: 233-244 (2012) DOI: 10.7546/giq-13-2012-233-244

Abstract

We consider a Riemannian manifold $M$ (dim$M\geq 3$), which is flat or has negative sectional curvature. We suppose that there is a closed and connected subgroup $G$ of Iso$(M)$ such that dim$({M}/{G})=2$. Then we study some topological properties of $M$ and the orbits of the action of $G$ on $M$.