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October, 2014 On the stability of locally conformal Kähler structures
Ryushi Goto
J. Math. Soc. Japan 66(4): 1375-1401 (October, 2014). DOI: 10.2969/jmsj/06641375


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 $b_2=0$.


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Ryushi Goto. "On the stability of locally conformal Kähler structures." J. Math. Soc. Japan 66 (4) 1375 - 1401, October, 2014.


Published: October, 2014
First available in Project Euclid: 23 October 2014

zbMATH: 1310.53062
MathSciNet: MR3272602
Digital Object Identifier: 10.2969/jmsj/06641375

Primary: 53C55
Secondary: 32G05

Keywords: deformation theory , locally conformally Kähler metrics , non-Kähler manifolds

Rights: Copyright © 2014 Mathematical Society of Japan


Vol.66 • No. 4 • October, 2014
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