On the stability of locally conformal Kaehler structures

Details On the stability of locally conformal Kaehler structures On the stability of locally conformal Kaehler structures

2010-12-10

arxiv.org/abs/1012.2285v1

Mathematics

Differential Geometry

26 pages

Scientific paper

In this article we develop a new approach to the problem of the stability of locally conformally K\"ahler structures (l.c.k structures) under small deformations of complex structures and deformations of flat line bundles. We show that under the certain cohomological condition the stability of l.c.k structures does hold. We apply our approach to Hopf manifolds and its generalizations 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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