18th November 2010, 1100 MC206

**Emeritus Professor Dmitri Alekseevski**

from

University of Edinburgh

will speak on

Quantizable Kähler Geometry, Sasakian Geometry, Conical Kähler Geometry and Locally Conformal Kähler Geometry

We discuss relations between these four types of geometries. In particular, we associate with a quantizable Kähler manifold *M* a principal bundle *S* → *M* with the structure group *A*=**S**^{1} or * R *and a contact form, θ, which, together with the complex structure,

*J*, of

*M*, defines a Sasakian structure on

*S*. The Riemannian cone

*C(S)*over

*S*has a canonical Kähler conical structure and its quotient carries a Vaisman locally conformal Kähler structure. We will discuss under which conditions this construction can be inverted. We consider also the homogeneous case and indicate some applications. This is joint work with V. Cortes, H. Hasegawa and Y. Kamishima