Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds

Abstract

We prove the non-existence of Vaisman metrics on some solvmanifolds with left-invariant complex structures. By this theorem, we show that Oeljeklaus-Toma manifolds does not admit Vaisman metrics.

12 page. arXiv admin note: substantial text overlap with arXiv:1104.3451. to appear in Bull. Lond. math. soc

References in corpus (5)

• Morse-Novikov cohomology of locally conformally Kähler manifolds
• Reduction of Vaisman structures in complex and quaternionic geometry
• Formality and hard Lefschetz property of aspherical manifolds
• Geometrical formality of solvmanifolds and solvable Lie type geometries
• Minimal models, formality and hard Lefschetz properties of solvmanifolds with local systems

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• Hopf surfaces in locally conformally Kahler manifolds with potential
• On the canonical bundle of complex solvmanifolds and applications to hypercomplex geometry
• On metric and cohomological properties of Oeljeklaus-Toma manifolds
• Homogeneous locally conformally Kähler manifolds
• Cohomologies of locally conformally symplectic manifolds and solvmanifolds
• Locally conformally Kähler solvmanifolds: a survey
• Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics
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• Remarks on Dolbeault cohomology of Oeljeklaus-Toma manifolds and Hodge theory
• Lefschetz coincidence numbers of solvmanifolds with Mostow conditions
• Cohomology of holomorphic line bundles and Hodge symmetry on Oeljeklaus-Toma manifolds
• The continuity equation for Hermitian metrics: Calabi estimates, Chern scalar curvature and Oeljeklaus-Toma manifolds
• The Lee--Gauduchon cone on complex manifolds