Locally conformally Kähler structures on four-dimensional solvable Lie algebras

Abstract

We classify and investigate locally conformally Kähler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on Oeljeklaus-Toma manifolds, and we also give a geometric interpretation of some of the $4$-dimensional structures in our classification.

arXiv commentMinor modifications added to the second version. To appear in Complex Manifolds

References in corpus (8)

• On Low-Dimensional Solvmanifolds
• Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds
• Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures
• Abelian complex structures on solvable Lie algebras
• LCK rank of locally conformally Kahler manifolds with potential
• Locally conformally Kähler structures on unimodular Lie groups
• Blowing-up points on l.c. K. manifolds
• Structure of locally conformally symplectic Lie algebras and solvmanifolds

Cited by in corpus (2)

• Curvature properties of Riemannian manifolds with skew-circulant structures
• Integrable LCK manifolds