Author:
Sferruzza Tommaso,Tomassini Adriano
Abstract
AbstractWe 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$$\mathcal {S}_M$$
S
M
and on the product of a Kodaira surface with an Inoue surface.
Funder
Università degli Studi di Parma
Publisher
Springer Science and Business Media LLC
Reference56 articles.
1. Alessandrini, L.: Classes of compact non-Kähler manifolds. C. R. Acad. Sci. Paris, Ser. I 349, 1089–1092 (2011)
2. Alessandrini, L., Andreatta, M.: Closed transverse $$(p, p)$$-forms on compact complex manifolds. Compos. Math. 61, 181–200 (1987). (Erratum 63 (1987), 143)
3. Alessandrini, L.: Holomorphic submersions onto Kähler or balanced manifolds. Tohoku Math. J. 68, 607–619 (2016)
4. Alessandrini, L.: Modifications of generalized $$p$$-Kähler manifolds. J. Geom. Anal. 27, 947–967 (2017)
5. Alessandrini, L.: Proper modifications of generalized p-Kähler manifolds. J. Geom. Anal. 27, 947–967 (2017)