Andrea Gambioli - Profile on Academia.edu (original) (raw)

Uploads

Papers by Andrea Gambioli

Research paper thumbnail of Eight-dimensional SU(3)-manifolds of cohomogeneity one

arXiv (Cornell University), Nov 27, 2006

In this paper, we classify 8-dimensional manifolds M admitting an SU (3) action of cohomogeneity ... more In this paper, we classify 8-dimensional manifolds M admitting an SU (3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) M/G ∼ = S 1 and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU (3) and to 8-dimensional quaternion-Kähler spaces.

Research paper thumbnail of UK-Japan Winter School 2004 : geometry and analysis towards quantum theory

UK-Japan Winter School 2004 : geometry and analysis towards quantum theory

Research paper thumbnail of Grassmannians, Lie algebras and quaternionic geometry

Grassmannians, Lie algebras and quaternionic geometry

Research paper thumbnail of Special geometries associated to quaternion-Kähler 8-manifolds

Journal of Geometry and Physics, 2015

We develop a calculus of differential forms on a quaternion-Kähler manifold M 4n admitting an iso... more We develop a calculus of differential forms on a quaternion-Kähler manifold M 4n admitting an isometric circle action. This is used to study three fundamental examples of such actions on the quaternionic projective plane and the construction of G 2 and half-flat structures on quotients of M 8 and its hypersurfaces.

Research paper thumbnail of SU(3)-manifolds of cohomogeneity one

SU(3)-manifolds of cohomogeneity one

Annals of Global Analysis and Geometry, 2007

ABSTRACT In this article, we classify 7- and 8-dimensional manifolds M admitting an SU(3) action ... more ABSTRACT In this article, we classify 7- and 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) M/G @ S1{M/G\cong S^{1}} and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU(3) and to 8-dimensional quaternion-Kähler spaces, and links between dimension 7 and 8 given by circle actions.

Research paper thumbnail of Eight-dimensional SU(3)-manifolds of cohomogeneity one

In this paper, we classify 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity o... more In this paper, we classify 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0,1], and (ii) M/G=S^1 and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU(3) and to 8-dimensional quaternion-Kahler spaces.

Research paper thumbnail of Latent Quaternionic Geometry

In this article we discuss the interaction between the geometry of a quaternion-Kähler manifold M... more In this article we discuss the interaction between the geometry of a quaternion-Kähler manifold M and that of the Grassmannian G3(g) of oriented 3-dimensional subspaces of a compact Lie algebra g. This interplay is described mainly through the moment mapping induced by the action of a group G of quaternionic isometries on M. We give an alternative expression for the endomorphisms I1, I2, I3, both in terms of the holonomy representation of M and the structure of the Grassmannian’s tangent space. A correspondence between the solutions of respective twistor-type equations on M and G3(g) is provided. MSC classification: 53C26; 53C35, 53C42, 53C28, 22E46, 57S25. 1

Research paper thumbnail of Eight-dimensional SU(3)-manifolds of

In this paper, we classify 8-dimensional manifolds M admitting an SU (3) action of cohomogeneity ... more In this paper, we classify 8-dimensional manifolds M admitting an SU (3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) M/G ∼ = S 1 and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU (3) and to 8-dimensional quaternion-Kähler spaces.

Research paper thumbnail of Eight-dimensional SU(3)-manifolds of cohomogeneity one

arXiv (Cornell University), Nov 27, 2006

In this paper, we classify 8-dimensional manifolds M admitting an SU (3) action of cohomogeneity ... more In this paper, we classify 8-dimensional manifolds M admitting an SU (3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) M/G ∼ = S 1 and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU (3) and to 8-dimensional quaternion-Kähler spaces.

Research paper thumbnail of UK-Japan Winter School 2004 : geometry and analysis towards quantum theory

UK-Japan Winter School 2004 : geometry and analysis towards quantum theory

Research paper thumbnail of Grassmannians, Lie algebras and quaternionic geometry

Grassmannians, Lie algebras and quaternionic geometry

Research paper thumbnail of Special geometries associated to quaternion-Kähler 8-manifolds

Journal of Geometry and Physics, 2015

We develop a calculus of differential forms on a quaternion-Kähler manifold M 4n admitting an iso... more We develop a calculus of differential forms on a quaternion-Kähler manifold M 4n admitting an isometric circle action. This is used to study three fundamental examples of such actions on the quaternionic projective plane and the construction of G 2 and half-flat structures on quotients of M 8 and its hypersurfaces.

Research paper thumbnail of SU(3)-manifolds of cohomogeneity one

SU(3)-manifolds of cohomogeneity one

Annals of Global Analysis and Geometry, 2007

ABSTRACT In this article, we classify 7- and 8-dimensional manifolds M admitting an SU(3) action ... more ABSTRACT In this article, we classify 7- and 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) M/G @ S1{M/G\cong S^{1}} and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU(3) and to 8-dimensional quaternion-Kähler spaces, and links between dimension 7 and 8 given by circle actions.

Research paper thumbnail of Eight-dimensional SU(3)-manifolds of cohomogeneity one

In this paper, we classify 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity o... more In this paper, we classify 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0,1], and (ii) M/G=S^1 and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU(3) and to 8-dimensional quaternion-Kahler spaces.

Research paper thumbnail of Latent Quaternionic Geometry

In this article we discuss the interaction between the geometry of a quaternion-Kähler manifold M... more In this article we discuss the interaction between the geometry of a quaternion-Kähler manifold M and that of the Grassmannian G3(g) of oriented 3-dimensional subspaces of a compact Lie algebra g. This interplay is described mainly through the moment mapping induced by the action of a group G of quaternionic isometries on M. We give an alternative expression for the endomorphisms I1, I2, I3, both in terms of the holonomy representation of M and the structure of the Grassmannian’s tangent space. A correspondence between the solutions of respective twistor-type equations on M and G3(g) is provided. MSC classification: 53C26; 53C35, 53C42, 53C28, 22E46, 57S25. 1

Research paper thumbnail of Eight-dimensional SU(3)-manifolds of

In this paper, we classify 8-dimensional manifolds M admitting an SU (3) action of cohomogeneity ... more In this paper, we classify 8-dimensional manifolds M admitting an SU (3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) M/G ∼ = S 1 and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU (3) and to 8-dimensional quaternion-Kähler spaces.