Homogeneous Weyl connections of non-positive curvature

Geometrically Formal Homogeneous Metrics of Positive Curvature

A Riemannian manifold is called geometrically formal if the wedge product of harmonic forms is again harmonic, which implies in the compact case that the manifold is topologically formal in the sense of rational homotopy theory. A manifold admitting a Riemannian metric of positive sectional curvature is conjectured to be topologically formal. Nonetheless, we show that among the homogeneous Riem...

Quasi-positive Curvature on Homogeneous Bundles

We provide new examples of manifolds which admit a Riemannian metric with sectional curvature nonnegative, and strictly positive at one point. Our examples include the unit tangent bundles of CP, HP and CaP, and a family of lens space bundles over CP.

Obstruction to Positive Curvature on Homogeneous Bundles

Examples of almost-positively and quasi-positively curved spaces of the form M = H\((G, h) × F ) were discovered recently [9],[8]. Here h is a left-invariant metric on a compact Lie group G, F is a compact Riemannian manifold on which the subgroup H ⊂ G acts isometrically on the left, and M is the orbit space of the diagonal left action of H on (G, h)×F with the induced Riemannian submersion me...

of non-positive Gaussian curvature

On the Geometry of Homogeneous Spaces of Positive Curvature

This Master’s thesis is a study of some of the geometric properties of Riemannian homogeneous spaces. These are Riemannian manifolds M equipped with a transitive group of isometries G, meaning that the local geometry of the manifold is the same at every point. In Section 1.3 we see that such spaces are diffeomorphic to the quotient G/K, where G is a Lie group and K is the isotropy group at the ...