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

N. K. Smolentsev

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arXiv · 1310.5395

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

N. K. Smolentsev

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Abstract

In this paper we consider left-invariant pseudo-Kähler structures on six-dimensional nilpotent Lie algebras. The explicit expressions of the canonical complex structures are calculated, and the curvature properties of the associated pseudo-Kähler metrics are investigated. It is proved that the associated pseudo-Kähler metric is Ricci-flat, that the curvature tensor has zero pseudo-Riemannian norm, and that the curvature tensor has some non-zero components that depend only on two or, at most, three parameters. The pseudo-Kähler structures obtained give basic models of pseudo-Kähler six-dimensional nilmanifolds.

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BibTeX RIS

N. K. Smolentsev. 2013-11-14. Canonical pseudo-Kähler structures on six-dimensional nilpotent Lie groups. https://arxiv.org/abs/1310.5395

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