Event description
Abstract: The existence of astheno-Kähler metrics on compact complex manifolds imposes certain cohomological restrictions. In particular, Chiose and Răsdeaconu [1] established inequalities relating the (0,1)-Bott–Chern and Aeppli numbers. More recently, Latorre and Ugarte [2] proved that, in complex dimension four, the existence of an astheno-Kähler metric on a nilmanifold implies that the underlying Lie group is at most 2-step nilpotent and that the complex structure is of special type. In this seminar, we show how the cohomological restrictions established in [1] can be used to extend these structural results to nilmanifolds of arbitrary complex dimension.
We then apply similar techniques to investigate the relationship between geometrically Bott–Chern formal metrics and strong Kähler with torsion (SKT) metrics on nilmanifolds.
Finally, we discuss some results concerning the existence of Hermitian metrics that are simultaneously (p)-SKT and (q)-SKT, for (1\leq p<q\leq n-1).
References
[1] I. Chiose and R. Răsdeaconu, Remarks on astheno-Kähler manifolds, Bott-Chern and Aeppli cohomology groups, Ann. Global Anal. Geom. 63 (2023), no. 3, Paper No. 24.
[2] A. Latorre and L. Ugarte, On astheno-Kähler nilmanifolds with balanced metrics, 2026. Preprint, arXiv:2606.28545.