Homogeneous Einstein Metrics on SO(n)
High Energy Physics - Theory
2010-01-22 v1 General Relativity and Quantum Cosmology
Differential Geometry
Abstract
It is well known that every compact simple Lie group G admits an Einstein metric that is invariant under the independent left and right actions of G. In addition to this bi-invariant metric, with G x G symmetry, it was shown by D'Atri and Ziller that every compact simple Lie group except SU(2) and SO(3) admits at least one further homogeneous Einstein metric, invariant under G x H, where H is some proper subgroup of G. In this paper we consider the Lie groups G=SO(n) for arbitrary n, and provide an explicit construction of (3k-4) inequivalent homogeneous Einstein metrics on SO(2k), and (3k-3) inequivalent homogeneous Einstein metrics on SO(2k+1).
Cite
@article{arxiv.1001.2776,
title = {Homogeneous Einstein Metrics on SO(n)},
author = {C. N. Pope},
journal= {arXiv preprint arXiv:1001.2776},
year = {2010}
}
Comments
7 pages