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A deformation of quaternionic hyperbolic space

Author: Megan M. Kerr
Journal: Proc. Amer. Math. Soc. 134 (2006), 559-569
MSC (2000): Primary 53C30, 53C25
Published electronically: July 8, 2005
MathSciNet review: 2176025
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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

Keywords: Differential geometry, Lie groups
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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