3,966 research outputs found
The index of symmetry of a flag manifold
We study the index of symmetry of a compact generalized flag manifold M=G/H
endowed with an invariant Kaehler structure. When the group G is simple we show
that the leaves of symmetry are irreducible Hermitian symmetric spaces and we
estimate their dimension
Construction of homogeneous Lagrangian submanifolds in \CP^n and Hamiltonian stability
We apply the concept of castling transform of prehomogeneous vector spaces to
produce new examples of minimal homogeneous Lagrangian submanifolds in the
complex projective space. Furthermore we verify the Hamiltonian stability of a
low dimensional example that can be obtained in this way
On moduli spaces of Ricci solitons
We study deformations of shrinking Ricci solitons on a compact manifold M,
generalising the classical theory of deformations of Einstein metrics. Using
appropriate notions of twisted slices S_f inside the space of all Riemannian
metrics on M, we define the infinitesimal solitonic deformations and the local
solitonic pre-moduli spaces. We prove the existence of a finite dimensional
submanifold of S_f x C^infty(M), which contains the pre-moduli space of
solitons around a fixed shrinking Ricci soliton as an analytic subset. We
define solitonic rigidity and give criteria which imply it.Comment: 18 page
Positively curved 7-dimensional manifolds
We deal with seven dimensional compact Riemannian manifolds of positive
curvature which admit a cohomogeneity one action by a compact Lie group G. We
prove that the manifold is diffeomorphic to a sphere if the dimension of the
semisimple part of G is bigger than 6.Comment: 7 pages; this new version contains one more important exampl
Spin structures and spectra of -manifolds
We give necessary and sufficient conditions for the existence of pin+, pin-
and spin structures on Riemannian manifolds with holonomy group . For
any n>3 (resp. n>5) we give examples of pairs of compact manifolds (resp.
compact orientable manifolds) M_1, M_2, non homeomorphic to each other, that
are Laplace isospectral on functions and on p-forms for any p and such that M_1
admits a pin+, or pin-, (resp. spin) structure whereas M_2 does not.Comment: 15 pages. Accepted for publication in Math.
Two-orbit K\"ahler manifolds and Morse Theory
We deal with compact K\"ahler manifolds acted on by a compact Lie group
of isometries, whose complexification K^\C has exactly one open and one
closed orbit in . If the -action is Hamiltonian, we obtain results on the
cohomology and the -equivariant cohomology of .Comment: 9 page
Totally geodesic orbits of isometries
We study cohomogeneity one Riemannian manifolds and we establish some simple
criterium to test when a singular orbit is totally geodesic. As an application,
we classify compact, positively curved Riemannian manifolds which are acted on
isometrically by a non semisimple Lie group with an hypersurface orbit.Comment: 13 page
Homogeneous toric bundles with positive first Chern class
A simple algebraic characterization of the Fano manifolds in the class of
homogeneous toric bundles over a flag manifold is provided in terms of
symplectic data.Comment: 14 page
Complex Asystatic actions of compact Lie Groups
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 acts complex asystatically on a K\"ahler manifold then
the -orbits are spherical. Finally we give the complete classification of
complex asystatic irreducible representations.Comment: 10 page
Kahler manifolds with large isometry group
We investigate compact Kahler manifolds, which are acted on by a semisimple
compact Lie group G of isometries with one hypersurface orbit. In case of
ordinary action and projectable complex structure, we set up a one to one
correspondence between such manifolds and abstract models. The Ricci tensor is
then computed and we fully characterize the Kahler-Einstein manifolds with an
ordinary cohomogeneity one action and projectable complex structure.Comment: 29 page
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