The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on May 9, 2023 at 2:00 pm (UTC+3)  in Room 478 of IMI.

A talk on:

Riemannian four-manifolds and twistor spaces: some rigidity results

 will be delivered by Davide Dameno, Department of Mathematics “Federigo Enriques”, University of Milan.

Everybody is invited.

Abstract. It is well-known that four-dimensional Riemannian manifolds carry many peculiar properties, which give rise to the existence of unique canonical metrics. In order to find conditions for the existence of such metrics, in 1978 Atiyah, Hitchin and Singer adapted Penrose’s construction of twistor spaces to the Riemannian context, paving the way for the study of many other characterizations of curvature properties for Riemannian four-manifolds. After giving an overview of the Riemannian and Hermitian structures of twistor spaces in the four-dimensional case, we present some new rigidity results for Riemannian four-manifolds whose twistor spaces satisfy specific vanishing conditions (such as Bochner-flatness). This is based on joint work with Professors Giovanni Catino and Paolo Mastrolia.