1,721,794 research outputs found

    Cyclic Phenomena for composition operators on Weighted Bergman Spaces

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    In the present paper we give a generalization to the family of Bergman Spaces with Weight GG, of several results obtained for the Hardy space, concerning the cyclic and hypercyclic behaviour of composition operators induced by a holomorphic self map of the open unit disc

    Two-orbit Kaehler manifolds and Morse Theory

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    We deal with compact K\"ahler manifolds MM acted on by a compact Lie group KK of isometries, whose complexification K^\C has exactly one open and one closed orbit in MM. If the KK-action is Hamiltonian, we obtain results on the cohomology and the KK-equivariant cohomology of MM

    Remarks on Kähler–Ricci solitons

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    We prove that a complex compact manifold endowed with a Ka ̈hler Ricci soliton cannot be isometrically embedded in a complex projective space CP^n in such a way that the Gauss map is rational, unless the metric is Einstein. This applies to hypersurfaces of complex compact homogeneous spaces canonically embedded in CP^n. We moreover obtain two curvature constraints for invariant Ka ̈hler Ricci solitons on complex manifolds acted on by a compact Lie group with cohomogeneity one

    Homogeneous Lagrangian submanifolds

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    We characterize isometric actions on compact Kaehler manifolds admitting a Lagrangian orbit, describing under which condition the Lagrangian orbit is unique. We furthermore give the complete classification of simple groups acting on the complex projective space with a Lagrangian orbit, and we give the explicit list of these orbits

    Actions of vanishing homogeneity rank on quaternionic-Kaehler projective spaces

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    We classify isometric actions of compact Lie groups on quaternionic-K\"ahler projective spaces with vanishing homogeneity rank. We also show that they are not in general quaternion-coisotropic

    A Hamiltonian stable minimal Lagrangian submanifold of projective space with non-parallel second fundamental form

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    In this note we show that Hamiltonian stable minimal Lagrangian submanifolds of projective space need not have parallel second fundamental form

    On deformations of Hamiltonian actions

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    In this paper we generalize to coisotropic actions of compact Lie groups a theorem of Guillemin on deformations of Hamiltonian structures on compact symplectic manifolds. We show how one can reconstruct from the moment polytope the symplectic form on the manifold
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