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Complex, Symplectic, and Contact Structures on Low-Dimensional Lie Groups

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Abstract

It is well known that on any Lie group, a left-invariant Riemannian structure can be defined. For other left-invariant geometric structures, for example, complex, symplectic, or contact structures, there are difficult obstructions for their existence, which have still not been overcome, although a lot of works were devoted to them. In recent years, substantial progress in this direction has been made; in particular, classification theorems for low-dimensional groups have been obtained. This paper is a brief review of left-invariant complex, symplectic, pseudo-Kählerian, and contact structures on low-dimensional Lie groups and classification results for Lie groups of dimension 4, 5, and 6.

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  1. Kemerovo State University, Kemerovo, Russia

    N. K. Smolentsev

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 127, Geometry, 2014.

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Smolentsev, N.K. Complex, Symplectic, and Contact Structures on Low-Dimensional Lie Groups. J Math Sci 207, 551–613 (2015). https://doi.org/10.1007/s10958-015-2385-6

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