2000 character limit reached
Symmetric and skew-symmetric complex structures (2101.11953v1)
Published 28 Jan 2021 in math.DG, hep-th, and math.SG
Abstract: On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-K\"ahler 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.