Symmetric and skew-symmetric complex structures

Abstract

On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-Kähler structures as symplectic forms with respect to which $J$ is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on 4-dimensional Lie algebras. We develop a method for constructing hypersymplectic structures from the above data. This allows us to obtain an example of a hypersymplectic structure on a 4-step nilmanifold.

20 pages, no figures. Comments are welcome!

References in corpus (8)

• Classification of abelian complex structures on 6-dimensional Lie algebras
• Double products and hypersymplectic structures on $R^{4n}$
• Invariant pseudo Kaehler metrics in dimension four
• Weak Mirror Symmetry of Complex Symplectic Algebras
• The geometry of recursion operators
• Construction of nice nilpotent Lie groups
• Special symplectic Lie groups and hypersymplectic Lie groups
• Complex structures on nilpotent Lie algebras and descending central series

Cited by in corpus (2)

• Pseudo-Kähler and hypersymplectic structures on semidirect products
• Complex Symplectic Lie Algebras with Large Abelian Subalgebras