Metric connections with parallel torsion

Abstract: The torsion of every metric connection on a Riemannian manifold has three components: one totally skew-symmetric, one of vectorial type, and one of twistorial type. In the first part of the talk I will explain the classification of complete simply connected Riemannian manifolds carrying a metric connection whose torsion is parallel, has non-zero vectorial component and vanishing twistorial component. In the second part I will describe the case where the only non-vanishing component of the torsion is totally skew-symmetric. Although apparently simpler than the previous case, the situation here is much more involved and a complete classification is currently not available. The talk is based on joint works with Mihaela Pilca and Uwe Semmelmann.

differential geometry

Audience: researchers in the topic

Differential Geometry Seminar Torino

Series comments: This is a hybrid seminar organized by the Differential Geometry groups of Università and Politecnico di Torino.

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