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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A deformation of quaternionic hyperbolic space
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by Megan M. Kerr PDF
Proc. Amer. Math. Soc. 134 (2006), 559-569 Request permission

Abstract:

We construct a continuous family of new homogeneous Einstein spaces with negative Ricci curvature, obtained by deforming from the quaternionic hyperbolic space of real dimension 12. We give an explicit description of this family, which is made up of Einstein solvmanifolds which share the same algebraic structure (eigenvalue type) as the rank one symmetric space $\mathbf {H}H^3$. This deformation includes a continuous family of new homogeneous Einstein spaces with negative sectional curvature.
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Additional Information
  • Megan M. Kerr
  • Affiliation: Department of Mathematics, Wellesley College, 106 Central St., Wellesley, Massachusetts 02481
  • Email: mkerr@wellesley.edu
  • Received by editor(s): February 1, 2002
  • Received by editor(s) in revised form: September 28, 2004
  • Published electronically: July 8, 2005
  • Additional Notes: The author was supported by the Clare Boothe Luce Foundation and by the Radcliffe Institute for Advanced Study.
  • Communicated by: Jon G. Wolfson
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 559-569
  • MSC (2000): Primary 53C30, 53C25
  • DOI: https://doi.org/10.1090/S0002-9939-05-08022-6
  • MathSciNet review: 2176025