Homogeneous Einstein Metrics on SO(n)

C. N. Pope

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arXiv · 1001.2776

Homogeneous Einstein Metrics on SO(n)

C. N. Pope

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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).

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C. N. Pope. 2010-01-18. Homogeneous Einstein Metrics on SO(n). https://arxiv.org/abs/1001.2776

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