Dept Math & Stat UiT, Forskningsparken B459
  27 Feb 2025 Wed

14:00-16:00

Omid Makhmali (UiT)

"Pre-Kahler structures and finite-nondegeneracy"

We define pre-Kahler structures on a complex manifold and motivate their study by noting that they are naturally induced on complex submanifolds of a pseudo-Kahler manifold and also arise as symmetry reductions of CR structures of hypersurface type that may not be Levi nondegenerate.

Mimicking the notion of k-nondegeneracy in the CR setting, we define k-nondegenerate pre-Kahler structures, which turn out to have finite-dimensional symmetry algebra. The correspondence between Sasakian and Kahler structures, arising either as the symmetry reduction or as the metric cone, is generalized to the pre-Kahler setting.

Lastly, as the lowest dimensional non-Kahler pre-Kahler case, we analyze 2-nondegenerate pre-Kahler structures on complex surfaces and give a solution of their equivalence problem in terms of a Cartan geometry. After providing parametric expressions for their essential invariants in terms of a pre-Kahler potential, we give examples and analyze a double fibration that they naturally define.

This is a joint work with David Sykes.