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Canonical almost pseudo-K\"{a}hler structures on six-dimensional nilpotent Lie groups by Smolentsev, N. K. is a scholarly article available to read on EtoBox.

What is Canonical almost pseudo-K\"{a}hler structures on six-dimensional nilpotent Lie groups about?

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-K\"{a}hler 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-K\"{a}hler metrics, and we study their geometrical properties.

Author

Smolentsev, N. K.

Published

2013

Language

EN