Locally conformally symplectic convexity

Florin Belgun; Oliver Goertsches; David Petrecca

doi:10.1016/j.geomphys.2018.10.001

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arXiv · 1805.00218

Locally conformally symplectic convexity

Florin Belgun·Oliver Goertsches·David Petrecca

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Abstract

We investigate special lcs and twisted Hamiltonian torus actions on strict lcs manifolds and characterize them geometrically in terms of the minimal presentation. We prove a convexity theorem for the corresponding twisted moment map, establishing thus an analog of the symplectic convexity theorem of Atiyah and Guillemin-Sternberg. We also prove similar results for the symplectic moment map (defined on the minimal presentation) whose image is then a convex cone. In the special case of a compact toric Vaisman manifold, we obtain a structure theorem.

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BibTeX RIS

Florin Belgun, Oliver Goertsches, David Petrecca. 2018-05-01. Locally conformally symplectic convexity. https://doi.org/10.1016/j.geomphys.2018.10.001

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