A Hermitian metric on a complex manifold of complex dimension n is called astheno-Kahler if its fundamental 2-form F satisfies the condition partial derivative partial derivative F(n-2) = 0. If n = 3, then the metric is strong KT, that is, F is partial derivative partial derivative-closed. By using blow-ups and the twist construction, we construct simply connected astheno-Kahler manifolds of complex dimension n > 3. Moreover, we construct a family of astheno-Kahler (non-strong KT) 2-step nilmanifolds of complex dimension 4 and we study deformations of strong KT structures on nilmanifolds of complex dimension 3. Finally, we study the relation between the astheno-Kahler condition and the (locally) conformally balanced condition and we provide examples of locally conformally balanced astheno-Kahler metrics on T(2)-bundles over (non-Kahler) homogeneous complex surfaces.

On astheno-Kähler metrics / A., Fino; Tomassini, Adriano. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 83:2(2011), pp. 290-308. [10.1112/jlms/jdq066]

On astheno-Kähler metrics

TOMASSINI, Adriano
2011-01-01

Abstract

A Hermitian metric on a complex manifold of complex dimension n is called astheno-Kahler if its fundamental 2-form F satisfies the condition partial derivative partial derivative F(n-2) = 0. If n = 3, then the metric is strong KT, that is, F is partial derivative partial derivative-closed. By using blow-ups and the twist construction, we construct simply connected astheno-Kahler manifolds of complex dimension n > 3. Moreover, we construct a family of astheno-Kahler (non-strong KT) 2-step nilmanifolds of complex dimension 4 and we study deformations of strong KT structures on nilmanifolds of complex dimension 3. Finally, we study the relation between the astheno-Kahler condition and the (locally) conformally balanced condition and we provide examples of locally conformally balanced astheno-Kahler metrics on T(2)-bundles over (non-Kahler) homogeneous complex surfaces.
On astheno-Kähler metrics / A., Fino; Tomassini, Adriano. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 83:2(2011), pp. 290-308. [10.1112/jlms/jdq066]
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/11381/2379006
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
  • ???jsp.display-item.citation.isi??? 25
social impact