منابع مشابه
On the Moment Map on Symplectic Manifolds
We consider a connected symplectic manifold M acted on by a connected Lie group G in a Hamiltonian fashion. If G is compact, we prove give an Equivalence Theorem for the symplectic manifolds whose squared moment map ‖ μ ‖ is constant. This result works also in the almost-Kähler setting. Then we study the case when G is a non compact Lie group acting properly on M and we prove a splitting result...
متن کاملA Note on the Moment Map on Symplectic Manifolds
We consider a connected symplectic manifold M acted on by a connected Lie group G in a Hamiltonian fashion. If G is compact we study the smooth function f =‖ μ ‖. We prove that if a point x ∈ M realizes a local maximum of the squared moment map ‖ μ ‖ then the orbit Gx is symplectic and Gμ(μ(x)) is G-equivariantly symplectomorphic to a product of a flag manifold and a symplectic manifold which i...
متن کاملA Note on the Moment Map on Compact Kähler Manifolds
We consider compact Kähler manifolds acted on by a connected compact Lie group K of isometries in a Hamiltonian fashion. We prove that the squared moment map ||μ|| is constant if and only if the manifold is biholomorphically and K-equivariantly isometric to a product of a flag manifold and a compact Kähler manifold which is acted on trivially by K. The authors do not know whether the compactnes...
متن کاملIsolated Fixed Points and Moment Maps on Symplectic Manifolds
Let (M, ω) be a compact connected symplectic manifold of dimension 2n equipped with a symplectic circle action. In this paper we show that if the fixed point set is non-empty and isolated then the symplectic circle action must be Hamiltonian. This extends the results of Tolman–Weitsman and McDuff, and proves their conjecture affirmatively. The main strategy is to use a variant of the Euler numb...
متن کاملToeplitz Operators on Symplectic Manifolds
We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established. 0. Introduction Quant...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2009
ISSN: 1370-1444
DOI: 10.36045/bbms/1235574195