New homogeneous Einstein metrics of negative Ricci curvature

Details New homogeneous Einstein metrics of negative Ricci curvature New homogeneous Einstein metrics of negative Ricci curvature

1999-08-17

arxiv.org/abs/math/9908089v1

Mathematics

Differential Geometry

19 pages

Scientific paper

We construct new homogeneous Einstein spaces with negative Ricci curvature in two ways: First, we give a method for classifying and constructing a class of rank one Einstein solvmanifolds whose derived algebras are two-step nilpotent. As an application, we describe an explicit continuous family of ten-dimensional Einstein manifolds with a two-dimensional parameter space, including a continuous subfamily of manifolds with negative sectional curvature. Secondly, we obtain new examples of non-symmetric Einstein solvmanifolds by modifying the algebraic structure of non-compact irreducible symmetric spaces of rank greater than one, preserving the (constant) Ricci curvature.

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