New Einstein metrics on the Lie group SO(n) which are not naturally reductive

2015/11/25 by Andreas Arvanitoyeorgos, Yusuke Sakane, Marina Statha · 1 citation
Mathematics · #math.DG #msc:53C25 #msc:53C30

paper · pdf

published as Geom. Imaging Comput. 2 (2) (2015) · 25 pages. arXiv admin note: text overlap with arXiv:1311.1579

arxiv created 2015/11/25 · arxiv updated 2016/02/09

Abstract

We obtain new invariant Einstein metrics on the compact Lie groups SO(n) (n ≥ 7) which are not naturally reductive. This is achieved by imposing certain symmetry assumptions in the set of all left-invariant metrics on SO(n) and by computing the Ricci tensor for such metrics. The Einstein metrics are obtained as solutions of systems polynomial equations, which we manipulate by symbolic computations using Gröbner bases.

Citations

• New homogeneous Einstein metrics on Stiefel manifolds

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