Deformations of astheno-K\'ahler metrics
| Autor: | Sferruzza, Tommaso |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | The property of admitting an astheno-K\"ahler metric is not stable under the action of small deformations of the complex structure of a compact complex manifold. In this paper, we prove necessary cohomological conditions for the existence of curves of astheno-K\"ahler metrics along curves of deformations starting from an initial compact complex manifold endowed with an astheno-K\"ahler metric. Furthermore, we apply our results providing obstructions to the existence of curves of astheno-K\"ahler metrics on two different families of real $8$-dimensional nilmanifolds endowed with invariant nilpotent complex structures. Comment: 18 pages |
| Databáze: | arXiv |
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