Alladi Ramakrishnan Hall

Group actions and non-Kaehler complex manifolds

Mainak Poddar

METU-NCC

We give new examples of complex manifolds
that are not Kahler,and therefore can not be projective algebraic
varieties. Well-known classical examples of such manifolds include the product of two odd dimensional spheres (due to Hopf and
Calabi-Eckmann), compact non-Abelian Lie groups of even dimension (due to Wang and Samelson), etc. Our construction is a generalization of the Lie group case to certain principal
bundles and more generally, to certain group actions. This is a joint work with Ajay Singh Thakur.