#### 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.

Done