Buongiorno,
segnalo che giovedì 23 maggio alle 14.30 in aula seminari Romeo Segnan Dalmasso (Università di Milano Bicocca) terrà un seminario dal titolo
*Harmful structures and Killing spinors*
di cui riporto l'abstract:
The existence of Killing spinors on a given manifold imposes strict conditions on its geometry. In the Riemannian setting in particular, this implies, for example, that the metric is Einstein. In the pseudo-Riemannian setting, the situation is less studied, nor as strict, for instance the metric need not be Einstein. In this talk, after an introduction to the language of spinors and some history concerning their study, I will present a new result concerning the existence of a Killing spinor on a pseudo-Riemannian manifold (Z, h). I will show that the existence on (Z, h) implies the existence of a pair of spinors (\psi, \phi) in the spinor bundle of an embedded (non-degenerate) hypersurface (M, g) satisfying a coupled PDE system involving the Weingarten operator of the embedding A, which will be called real or imaginary weakly /harmful structure/, depending on the signature of the normal vector-field to (M, g). The embedding process will require an additional technical condition, namely d tr A+\delta A = 0, and the assumption that the metric and the Weingarten operator are real analytic tensors. Some comments will be given on the special case of Lorentzian signature. Finally, I will present some work in progress regarding a (partial) classification in low dimension of harmful structures on homogeneous manifolds and the resulting cohomogeneity-one embeddings. This talk is based on a joint work with D. Conti and F.A. Rossi.
A presto
Diego