Cohomogeneity one Riemannian manifolds and Killing fields

AbstractThis paper is devoted to the study of isometries of cohomogeneity one Riemannian spaces, namely Riemannian manifolds acted on by a Lie group of isometries G with principal orbits of codimension one. We show that, for a class of such manifolds, every one parameter group of isometries preserves the foliation induced by the action of the Lie group G

Homogeneous Hypercomplex Structures and the Joyce's Construction

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 $M$.Comment: 11 page

On Moduli Spaces of Ricci Solitons

We study deformations of shrinking Ricci solitons on a compact manifold M, generalizing the classical theory of deformations of Einstein metrics. Using appropriate notions of twisted slices S 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, 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. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdA

Closed G2_2-structures with a transitive reductive group of automorphisms

We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G$_2$-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is one-dimensional and the manifold is the Riemannian product of a flat factor and a non-compact homogeneous six-dimensional manifold endowed with an invariant strictly symplectic half-flat SU(3)-structure