On astheno-Kaehler metrics
| Autor: | Fino, Anna, Tomassini, Adriano |
|---|---|
| Rok vydání: | 2008 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/jlms/jdq066 |
| Popis: | A Hermitian metric on a complex manifold of complex dimension $n$ is called {\em astheno-K\"ahler} if its fundamental $2$-form $F$ satisfies the condition $\partial \overline \partial F^{n - 2} =0$. If $n =3$, then the metric is {\em strong KT}, i.e. $F$ is $\partial \overline \partial$-closed. By using blow-ups and the twist construction, we construct simply-connected astheno-K\"ahler manifolds of complex dimension $n > 3$. Moreover, we construct a family of astheno-K\"ahler (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 astheno-K\"ahler condition and (locally) conformally balanced one and we provide examples of locally conformally balanced astheno-K\"ahler metrics on $\T^2$-bundles over (non-K\"ahler) homogeneous complex surfaces. Comment: 20 pages. To be published in J. Lond. Math. Soc |
| Databáze: | arXiv |
| Externí odkaz: |
|