On curvature homogeneous and locally homogeneous affine connections

Curvature Homogeneous Pseudo-riemannian Manifolds Which Are Not Locally Homogeneous

We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.

Cross Curvature Flow on Locally Homogeneous Three-manifolds (ii)

In this paper, we study the positive cross curvature flow on locally homogeneous 3-manifolds. We describe the long time behavior of these flows. We combine this with earlier results concerning the asymptotic behavior of the negative cross curvature flow to describe the two sided behavior of maximal solutions of the cross curvature flow on locally homogeneous 3-manifolds. We show that, typically...

Locally Homogeneous Geometric Manifolds

Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group. These locally homogeneous spaces later formed the context of Thurston’s 3-dimensional geometrization program. The basic problem is for a given topology Σ an...

Locally Homogeneous Graphs

For a connected graph G and point v of G, let G, be the subgraph induced by the points adjacent to v . This G is called locally Go if G, = Go for all points v of G. A graph is called locally homogeneous if it is locally Go for some Go. Recent work concerning local homogeneity has focused on two broad questions. First, for which Go does there exist a G that is locally Go? This has been settled f...

Zero - Entropy Affine Maps on Homogeneous Spaces