Deformations of astheno-Kähler metrics

Abstract

The property of admitting an astheno-Kähler metric is not stable under the action of small deformations of the complex structure of a compact complex manifold. In this study, we prove necessary cohomological conditions for the existence of curves of astheno-Kähler metrics along curves of deformations starting from an initial compact complex manifold endowed with an astheno-Kähler metric. Furthermore, we apply our results providing obstructions to the existence of curves of astheno-Kähler metrics on two different families of real eight-dimensional nilmanifolds endowed with invariant nilpotent complex structures.

Keywords

• astheno-kähler metric
• deformation of complex structure
• bott-chern cohomology
• 53c55
• 32g05
• 53b35