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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

Research paper thumbnail of Grassmannians, Lie algebras and quaternionic geometry

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

Journal of Geometry and Physics, 2015

Research paper thumbnail of 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

Research paper thumbnail of Grassmannians, Lie algebras and quaternionic geometry

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

Journal of Geometry and Physics, 2015

Research paper thumbnail of 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.