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Sep 22, 2013
09/13

by
Anna Gori; Fabio Podesta'

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We consider compact K\"ahler manifolds acted on by a connected compact Lie group $K$ of isometries in Hamiltonian fashion. We prove that the squared moment map $\|\mu\|^2$ is constant if and only if the manifold is biholomorphically and $K$-equivariantly isometric to a product of a flag manifold and a compact K\"ahler manifold which is acted on trivially by $K$. The authors do not know whether the compactness of $M$ is essential in the main theorem; more generally it would be...

Source: http://arxiv.org/abs/math/0310213v1

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159

Jul 20, 2013
07/13

by
Lucio Bedulli; Anna Gori

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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.

Source: http://arxiv.org/abs/math/0604169v2

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58

Sep 23, 2013
09/13

by
Anna Gori; Fabio Podesta

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In the present paper we introduce the notion of complex asystatic Hamiltonian action on a K\"ahler manifold. In the algebraic setting we prove that if a complex linear group $G$ acts complex asystatically on a K\"ahler manifold then the $G$-orbits are spherical. Finally we give the complete classification of complex asystatic irreducible representations.

Source: http://arxiv.org/abs/math/0411204v1

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89

Sep 24, 2013
09/13

by
Lucio Bedulli; Anna Gori

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We consider compact symplectic manifolds acted on effectively by a compact connected Lie group $K$ in a Hamiltonian fashion. We prove that the squared moment map $||\mu||^2$ is constant if and only if $K$ is semisimple and the manifold is $K$-equivariantly symplectomorphic to a product of a flag manifold and a compact symplectic manifold which is acted on trivially by $K$. In the almost-K\"ahler setting the symplectomorphism turns out to be an isometry.

Source: http://arxiv.org/abs/math/0412056v1

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47

Sep 23, 2013
09/13

by
Lucio Bedulli; Anna Gori

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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.

Source: http://arxiv.org/abs/math/0511015v1

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53

Sep 20, 2013
09/13

by
Lucio Bedulli; Anna Gori

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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.

Source: http://arxiv.org/abs/0802.0972v3

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70

Sep 22, 2013
09/13

by
Anna Gori; Fabio Podesta'

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

Source: http://arxiv.org/abs/math/0310178v1

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44

Sep 22, 2013
09/13

by
Lucio Bedulli; Anna Gori

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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.

Source: http://arxiv.org/abs/math/0603528v1

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78

Sep 19, 2013
09/13

by
Leonardo Biliotti; Anna Gori

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The main result of the paper is the complete classification of the compact connected Lie groups acting coisotropically on complex Grassmannians. This is used to determine the polar actions on the same manifolds.

Source: http://arxiv.org/abs/math/0304139v3

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5.0

Jun 29, 2018
06/18

by
Graziano Gentili; Anna Gori; Giulia Sarfatti

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The recent definition of slice regular function of several quaternionic variables suggests a new notion of quaternionic manifold. We give the definition of quaternionic regular manifold, as a space locally modeled on $\mathbb{H}^n$, in a slice regular sense. We exhibit some significant classes of examples, including manifolds which carry a quaternionic affine structure.

Topics: Complex Variables, Mathematics

Source: http://arxiv.org/abs/1612.03685

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3.0

Jun 29, 2018
06/18

by
Graziano Gentili; Anna Gori; Giulia Sarfatti

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In the present paper we introduce and study a new notion of toric manifold in the quaternionic setting. We develop a construction with which, starting from appropriate $m$-dimensional Delzant polytopes, we obtain manifolds of real dimension $4m$, acted on by $m$ copies of the group ${\rm Sp}(1)$ of unit quaternions. These manifolds are quaternionic regular and can be endowed with a $4$-plectic structure and a generalized moment map. Convexity properties of the image of the moment map are...

Topics: Complex Variables, Differential Geometry, Symplectic Geometry, Mathematics

Source: http://arxiv.org/abs/1612.03600

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51

Sep 23, 2013
09/13

by
Lucio Bedulli; Anna Gori; Fabio Podestà

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We prove that a maximal totally complex submanifold $N^{2n}$ of the quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a parallel submanifold, provided one of the following conditions is satisfied: (1) $N$ is the orbit of a compact Lie group of isometries, (2) the restricted normal holonomy is a proper subgroup of ${\rm U}(n)$.

Source: http://arxiv.org/abs/0810.0173v1

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52

Sep 22, 2013
09/13

by
Lucio Bedulli; Anna Gori; Fabio Podestà

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We prove that any invariant hypercomplex structure on a homogeneous space $M = G/L$ where $G$ is a compact Lie group is obtained via the Joyce's construction, provided that there exists a hyper-Hermitian naturally reductive invariant metric on $M$.

Source: http://arxiv.org/abs/1004.5238v1