Quaternionic hyperbolic space and nearby negatively curved
homogeneous Einstein manifolds
Megan Kerr
Wellesley College
Wednesday, December 5
2:30-3:30 pm, Room 4422
We construct a continuous family of new homogeneous Einstein
spaces with
negative Ricci curvature, obtained by deforming from quaternionic
hyperbolic space ${\Bbb H}H^3$. Recent work of Jens Heber shows that the
rank-one symmetric spaces of non-compact type come in surprisingly
large-dimensional moduli spaces of ``nearby'' Einstein manifolds,
homogeneous Einstein spaces with a related algebraic structure. We give
an explicit description of a family which is made up of Einstein
solvmanifolds which share the same algebraic structure (eigenvalue type)
as ${\Bbb H}H^3$. This deformation includes a continuous family of new
homogeneous Einstein spaces with negative sectional curvature.