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Description: |
In this talk, we will present a systematic investigation of manifolds that are Einstein for a connection ∇ with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any Einstein manifold with skew torsion has constant scalar curvature; and if it is complete of positive scalar ∇-curvature, it is necessarily compact and it has finite first fundamental group π1. We will then present large families of examples and discuss also when a Riemannian Einstein manifold can be Einstein with skew torsion. We will give examples of almost Hermitian, almost metric contact, and G2 manifolds that are Einstein with skew torsion. For example, we prove that any Einstein-Sasaki manifold and any 7-dimensional 3-Sasakian manifolds admit deformations into an Einstein metric with parallel skew torsion.
(This is joint work with Ilka Agricola, Philipps University - Marburg).
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