Canonical almost pseudo-Kähler structures on six-dimensional nilpotent Lie groups

Abstract

It is known that there are 34 classes of isomorphic connected simply connected six-dimensional nilpotent Lie groups. Of these, only 26 classes suppose left-invariant symplectic structures \cite{Goze-Khakim-Med}. In \cite{CFU2} it is shown that 14 classes of symplectic six-dimensional nilpotent Lie groups suppose compatible complex structures and, therefore, define pseudo-Kähler metrics. In this paper we show that on the remaining 12 classes of six-dimensional nilpotent symplectic Lie groups there are left-invariant almost pseudo-Kähler metrics, and we study their geometrical properties.

26 pages. arXiv admin note: text overlap with arXiv:1310.5395

References in corpus (2)

• Invariant pseudo Kaehler metrics in dimension four
• Complex structures on nilpotent Lie algebras

Cited by in corpus (2)

• On the moduli spaces of left invariant metrics on cotangent bundle of Heisenberg group
• Left-invariant almost para-complex structures on six-dimensional nilpotent Lie groups