On cohomological and formal properties of Strong K\'ahler with torsion and astheno-K\'ahler metrics

Autor:	Sferruzza, Tommaso, Tomassini, Adriano
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry 53C55 32C10
Druh dokumentu:	Working Paper
Popis:	We provide families of compact astheno-K\"ahler nilmanifolds and we study the behaviour of the complex blowup of such manifolds. We prove that the existence of an astheno-K\"ahler metric satisfying an extra differential condition is not preserved by blowup. We also study the interplay between Strong K\"ahler with torsion metrics and geometrically Bott-Chern metrics. We show that Fino-Parton-Salamon nilmanifolds are geometrically-Bott-Chern-formal, whereas we obtain negative results on the product of two copies of primary Kodaira surface, Inoue surface of type $\mathcal{S}_M$ and on the product of a Kodaira surface with an Inoue surface. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.06904 Zobrazit plný text záznamu View this record from Arxiv