We provide families of compact astheno-Kähler nilmanifolds and we study the behaviour of the complex blowup of such manifolds. We prove that the existence of an astheno-Kähler metric satisfying an extra differential condition is not preserved by blowup. We also study the interplay between Strong Kähler 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 SM and on the product of a Kodaira surface with an Inoue surface.

On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics / Sferruzza, T.; Tomassini, A.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 304:4(2023). [10.1007/s00209-023-03303-9]

On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics

Sferruzza T.;Tomassini A.
2023-01-01

Abstract

We provide families of compact astheno-Kähler nilmanifolds and we study the behaviour of the complex blowup of such manifolds. We prove that the existence of an astheno-Kähler metric satisfying an extra differential condition is not preserved by blowup. We also study the interplay between Strong Kähler 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 SM and on the product of a Kodaira surface with an Inoue surface.
2023
On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics / Sferruzza, T.; Tomassini, A.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 304:4(2023). [10.1007/s00209-023-03303-9]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2953118
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact