Geometry seminar: Prof. Legendre (Universite' Paul Sabatier,Toulouse), Kaehler reduction of product of spheres
Event Description:
Geometry seminar
Wednesday April 22 at 3 in SMLC 356
Speaker: Prof. Eveline Legendre, Universite' Paul Sabatier, Toulouse, France
Title: Kaehler reduction of product of spheres.
Contact person: Charles Boyer
Abstract:
I will explain a correspondence between labelled convex quadrilaterals and
T^4-invariant connections 1-form on S^3xS^3 having positive definite
differential on the standard CR structure of S^3xS^3. In rational case,
each of these structures define a natural Kaehler metric on the toric
orbifold associated to the labelled quadriateral we started with. Every
compact toric 4-orbifold with second Betti number 2 is concerned. This
construction generalizes the work of Webster and Bryant on product of
spheres and can be seen as an example of generalized Sasaki construction.
If I have the time I will speak about the generalisation of this on product
of odd-dimensional spheres. This is a joint work with V. Apostolov,
D.Calderbank and P. Gauduchon.