Homogeneous Einstein-like metrics on spheres and projective spaces

Projective Invariant Metrics for Einstein Spaces

Einstein Metrics on Spheres

Any sphere S admits a metric of constant sectional curvature. These canonical metrics are homogeneous and Einstein, that is the Ricci curvature is a constant multiple of the metric. The spheres S, m > 1 are known to have another Sp(m + 1)-homogeneous Einstein metric discovered by Jensen [Jen73]. In addition, S has a third Spin(9)-invariant homogeneous Einstein metric discovered by Bourguignon a...

Some New Homogeneous Einstein Metrics on Symmetric Spaces

We classify homogeneous Einstein metrics on compact irreducible symmetric spaces. In particular, we consider symmetric spaces with rank(M) > 1, not isometric to a compact Lie group. Whenever there exists a closed proper subgroup G of Isom(M) acting transitively on M we nd all G-homogeneous (non-symmetric) Einstein metrics on M .

Sasakian Geometry and Einstein Metrics on Spheres

This paper is based on a talk presented by the first author at the Short Program on Riemannian Geometry that took place at the Centre de Recherche Mathématiques, Université de Montréal, during the period June 28-July 16, 2004. It is a report on our joint work with János Kollár [BGK03] concerning the existence of an abundance of Einstein metrics on odd dimensional spheres, including exotic spher...

Einstein Metrics on Tangent Bundles of Spheres

We give an elementary treatment of the existence of complete Kähler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n + 1)-sphere. Mathematics Subject Classification (2000) 53C