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