SO(n)\SO_0(n,1) has Positive Curvatures
Geometric Topology
2010-12-03 v1 Differential Geometry
Abstract
The Lie group SO_0(n, 1) has the left-invariant metric coming from the Killing-Cartan form. The maximal compact subgroup SO(n) of the isometry group acts from the left. The geometry of the quotient space of the homogeneous submersion SO_0(n, 1) -> SO(n)\SO_0(n, 1) is investigated. The space is expressed as a warped product. Its group of isometries and sectional curvatures are calculated.
Keywords
Cite
@article{arxiv.1012.0357,
title = {SO(n)\SO_0(n,1) has Positive Curvatures},
author = {Taechang Byun and Kyeonghee Jo and Kyung Bai Lee},
journal= {arXiv preprint arXiv:1012.0357},
year = {2010}
}