Equivariant Kählerian extensions of contact manifolds

DOI10.1515/CRELLE.2011.173zbMATH Open1264.32012arXiv1006.1109OpenAlexW2964289056MaRDI QIDQ4899180

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Publication date: 7 January 2013

Published in: (Search for Journal in Brave)

Abstract: For contact manifolds $(M,eta)$ a complexification $M^c$ is constructed to which the contact form $eta$ extends such that the exterior derivative of the extended form is K"ahlerian. In the case of a proper action of an extendable Lie group this construction is realized in an equivariant way. In a simultaneous stratification of $M$ and $M^c$ according to the istropy type, it is shown that the K"ahlerian reduction of the complexification can be seen as the complexification of the contact reduction.

Full work available at URL: https://arxiv.org/abs/1006.1109

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