We review the properties of the Morse-Novikov cohomology and compute it for all known compact complex surfaces with locally conformally Kähler metrics. We present explicit computations for the Inoue surfaces S0, S+, S- and classify the locally conformally Kähler (and the tamed locally conformally symplectic) forms on S0. We prove the nonexistence of LCK metrics with potential and more generally, of dθ-exact LCK metrics on Inoue surfaces and Oeljeklaus-Toma manifolds.
Otiman, A. (2018). Morse-Novikov cohomology of locally conformally Kähler surfaces. MATHEMATISCHE ZEITSCHRIFT, 289(1-2), 605-628 [10.1007/s00209-017-1968-y].
Morse-Novikov cohomology of locally conformally Kähler surfaces
Otiman A.
2018-01-01
Abstract
We review the properties of the Morse-Novikov cohomology and compute it for all known compact complex surfaces with locally conformally Kähler metrics. We present explicit computations for the Inoue surfaces S0, S+, S- and classify the locally conformally Kähler (and the tamed locally conformally symplectic) forms on S0. We prove the nonexistence of LCK metrics with potential and more generally, of dθ-exact LCK metrics on Inoue surfaces and Oeljeklaus-Toma manifolds.File in questo prodotto:
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