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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

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Volume 18, Issue 4


New homogeneous Einstein metrics on quaternionic Stiefel manifolds

Andreas Arvanitoyeorgos / Yusuke Sakane
  • Osaka University, Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Suita, Osaka 565-0871, Japan
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/ Marina Statha
Published Online: 2018-10-25 | DOI: https://doi.org/10.1515/advgeom-2018-0014


We consider invariant Einstein metrics on the quaternionic Stiefel manifold Vpn of all orthonormal p-frames in ℍn. This manifold is diffeomorphic to the homogeneous space Sp(n)/Sp(np) and its isotropy representation contains equivalent summands. We obtain new Einstein metrics on Vpn ≅ Sp(n)/Sp(np), where n = k1 + k2 + k3 and p = nk3. We view Vpn as a total space over the generalized Wallach space Sp(n)/(Sp(k1)×Sp(k2)×Sp(k3)) and over the generalized flag manifold Sp(n)/(U(p)×Sp(np)).

Keywords: Homogeneous space; Einstein metric; quaternionic Stiefel manifold; generalized Wallach space; generalized flag manifold; isotropy representation, Gröbner basis

MSC 2010: Primary 53C25; Secondary 53C30; 13P10; 65H10; 68W30


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About the article

Received: 2016-09-05

Published Online: 2018-10-25

Published in Print: 2018-10-25

Funding: The first and third authors were supported by Grant #E.037 from the Research Committee of the University of Patras (Programme K. Karatheodori). The second author was supported by JSPS KAKENHI Grant Number JP16K05130. The first author was supported by a grand from the Empirikion Foundation in Athens, Greece.

Citation Information: Advances in Geometry, Volume 18, Issue 4, Pages 509–524, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0014.

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