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Locally conformally Kähler manifolds and their cohomology

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Alexandra Otiman
University of Bucharest/MPIM
Thu, 2018-02-01 16:30 - 17:30
MPIM Lecture Hall

A Hermitian metric on a complex manifold is locally conformally Kähler (LCK) if it is conformal to a Kähler metric around each point.
Many of the complex non-Kähler manifolds admit such a metric. In this talk, I will discuss several examples, focusing on complex surfaces.

LCK manifolds provide a natural context for the study of twisted cohomology, also known as Morse-Novikov, which is the cohomology with values in a flat bundle. We compute it for Inoue surfaces and explain the relation between the twisted cohomology and their LCK geometry.

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