Bulletin of the Belgian Mathematical Society - Simon Stevin

On the moment map on symplectic manifolds

Leonardo Biliotti

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Abstract

We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion by a connected Lie group $G$. If $G$ is compact, then we characterize the symplectic manifolds whose squared moment map is constant. We also give a sufficient condition for $G$ to admit a symplectic orbit. Then we study the case when $G$ is a non-compact Lie group proving splitting results for symplectic manifolds.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 1 (2009), 107-116.

Dates
First available in Project Euclid: 25 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1235574195

Digital Object Identifier
doi:10.36045/bbms/1235574195

Mathematical Reviews number (MathSciNet)
MR2498962

Zentralblatt MATH identifier
1160.53373

Subjects
Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 57S15: Compact Lie groups of differentiable transformations

Keywords
moment map symplectic and almost-Kähler manifolds

Citation

Biliotti, Leonardo. On the moment map on symplectic manifolds. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 1, 107--116. doi:10.36045/bbms/1235574195. https://projecteuclid.org/euclid.bbms/1235574195


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