Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Morse-Novikov cohomology of locally conformally K\"ahler manifolds   A locally conformally Kahler (LCK) manifold is a complex manifold admitting a
Kahler covering, with the monodromy acting on this covering by homotheties. We
define three cohomology invariants, the Lee class, the Morse-Novikov class, and
the Bott-Chern class, of an LCK-structure. These invariants together play the
same role as the Kahler class in Kahler geometry. If these classes for two
LCK-structures coincide, the difference between these structures can be
expressed by a smooth potential, similar to the Kahler case. We show that the
Morse-Novikov class and the Bott-Chern class of a Vaisman manifold vanishes.
Moreover, for any LCK-structure on a Vaisman manifold, we prove that its
Morse-Novikov class vanishes. We show that a compact LCK-manifold $M$ with
vanishing Bott-Chern class admits a holomorphic embedding to a Hopf manifold,
if $\dim_\C M \geq 3$, a result which parallels the Kodaira embedding theorem.

29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: physics