Event description
Abstract: In 1953, Calabi and Eckmann gave an example of a compact complex manifold which cannot admit a Kähler structure. In this talk we describe a possible generalization of their construction using Kähler Lie group actions and momentum maps.
This allows us to define almost complex structures on product manifolds, and we prove that such structures are integrable if and only if the group acting is Abelian.
When the almost complex structure is integrable, we construct holomorphic charts of the product manifold.
We conclude by presenting two possible applications: the complex Stiefel manifold and the infinite Calabi-Eckmann manifold.
This is a joint work with Prof. Leonardo Biliotti.