# Homogeneous Einstein Metrics on SOn - High Energy Physics - Theory

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Abstract: It is well known that every compact simple Lie group G admits an Einsteinmetric that is invariant under the independent left and right actions of G. Inaddition to this bi-invariant metric, with G x G symmetry, it was shown byD-Atri and Ziller that every compact simple Lie group except SU2 and SO3admits 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 groupsG=SOn for arbitrary n, and provide an explicit construction of 3k-4inequivalent homogeneous Einstein metrics on SO2k, and 3k-3 inequivalenthomogeneous Einstein metrics on SO2k+1.

Author: ** C.N. Pope**

Source: https://arxiv.org/