New homogeneous Einstein metrics on Stiefel manifolds

2013/11/07 by Andreas Arvanitoyeorgos, Yusuke Sakane, Marina Statha · 3 citations
Mathematics · #math.DG #msc:53C25 #msc:53C30 #msc:13P10 #msc:65H10 #msc:68W30

paper · pdf

published as Differential Geom. Appl. 35 (2014) S2-S18

arxiv created 2013/11/07 · arxiv updated 2015/11/26

Abstract

We consider invariant Einstein metrics on the Stiefel manifold V_q\bbR ⁿ of all orthonormal q-frames in \bbRⁿ. This manifold is diffeomorphic to the homogeneous space \SO(n)/\SO(n-q) and its isotropy representation contains equivalent summands. %This causes difficulty in the description of all \SO(n)-invariant metrics. We prove, by assuming additional symmetries, that V₄\bbRⁿ (n≥ 6) admits at least four \SO(n)-invariant Einstein metrics, two of which are Jensen's metrics and the other two are new metrics. Moreover, we prove that V₅\bbR⁷ admits at least six invariant Einstein metrics, two of which are Jensen's metrics and the other four are new metrics.

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