Morse-Novikov cohomology of locally conformally Kähler surfaces

2018/01/01 by Alexandra Otiman · 4 citations
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows

paper · doi:10.1007/s00209-017-1968-y

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.

Cited by

• Rigidity of Lie affine foliations
• Existence Criteria for LCK Metrics
• Morse-Novikov cohomology of almost nonnegatively curved manifolds
• Holomorphic Euler number of Kahler manifolds with almost nonnegative Ricci curvature

Related

• Morse-Novikov cohomology of locally conformally Kähler surfaces
• Morse-Novikov cohomology of closed one-forms of rank 1
• On the Lee classes of locally conformally symplectic complex surfaces
• On a question of Vaisman concerning complex surfaces
• De Rham and twisted cohomology of Oeljeklaus-Toma manifolds