Deformations of astheno-Kähler metrics-Reference-Cited by-同舟云学术

Deformations of astheno-Kähler metrics

Published:2023-01-01 Issue:1 Volume:10 Page:
ISSN:2300-7443
Container-title:Complex Manifolds
language:en
Short-container-title:

Author:

Sferruzza Tommaso¹

Affiliation:

1. Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Unità di Matematica e Informatica, Università degli studi di Parma , Parco Area delle Scienze, 53/A, 43124 Parma , Italy

Abstract

AbstractThe property of admitting an astheno-Kähler metric is not stable under the action of small deformations of the complex structure of a compact complex manifold. In this study, we prove necessary cohomological conditions for the existence of curves of astheno-Kähler metrics along curves of deformations starting from an initial compact complex manifold endowed with an astheno-Kähler metric. Furthermore, we apply our results providing obstructions to the existence of curves of astheno-Kähler metrics on two different families of real eight-dimensional nilmanifolds endowed with invariant nilpotent complex structures.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/coma-2023-0102/pdf

Reference33 articles.

1. L. Alessandrini and M. Andreatta, Closed transverse (p,p)-forms on compact complex manifolds, Compositio Math. 61 (1987), 181–200; Erratum 63 (1987), 143.

2. L. Alessandrini and G. Bassanelli, Small deformations of a class of compact non-Kähler manifolds, Proc. Amer. Math. Soc. 109 (1990), no. 4, 1059–1062.

3. D. Angella, The cohomologies of the Iwasawa manifold and its small deformations, J. Geom. Anal. 23 (2013), 1355–1378.

4. D. Angella and H. Kasuya, Cohomologies of deformations of solvmanifolds and closedness of some properties, North-West. Eur. J. Math. 3 (2017), 75–105.

5. D. Angella and L. Ugarte, On small deformations of balanced manifolds, Differential Geom. Appl. 54 (2017), 464–474.