Journal of the Mathematical Society of Japan

On the stability of locally conformal Kähler structures

Ryushi Goto

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Abstract

In this article we develop a new approach to the problem of the stability of locally conformally Kähler structures (l.c.k structures) under small deformations of complex structures and deformations of flat line bundles. We show a cohomological criterion for the stability of l.c.k structures. We apply our approach to generalizations of Hopf manifolds to obtain the stability of l.c.k structures which do not have potential in general. We give an explicit description of the cohomological obstructions of the stability of l.c.k structures on Inoue surfaces with $b_2=0$.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 4 (2014), 1375-1401.

Dates
First available in Project Euclid: 23 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1414090245

Digital Object Identifier
doi:10.2969/jmsj/06641375

Mathematical Reviews number (MathSciNet)
MR3272602

Zentralblatt MATH identifier
1310.53062

Subjects
Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]
Secondary: 32G05: Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]

Keywords
locally conformally Kähler metrics non-Kähler manifolds deformation theory

Citation

Goto, Ryushi. On the stability of locally conformal Kähler structures. J. Math. Soc. Japan 66 (2014), no. 4, 1375--1401. doi:10.2969/jmsj/06641375. https://projecteuclid.org/euclid.jmsj/1414090245


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