Type II almost-homogeneous manifolds of cohomogeneity one

Existence of extremal metrics on almost homogeneous manifolds of cohomogeneity one – IV

This paper is the first of a series of papers in which we generalize our results in (Asian J. of Math. 4, 817–830 (2000); J. Geom. Anal. 12, 63–79 (2002); Intern. J. Math. 14, 259–287 (2003)) to the general complex compact almost homogeneous manifolds of real cohomogeneity one. In this paper we deal with the exceptional case of the G2 action (Cf. Intern. J. Math. 14, 259–287 (2003), p. 285). In...

Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One∗

Cohomogeneity One Einstein-sasaki 5-manifolds

We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly) hypo and half-flat evolution equations in higher dimensions. We use these equations to classify Einstein-Sasaki 5-manifolds of cohomogeneity one...

Non-negatively Curved Cohomogeneity One Manifolds

Non-negatively Curved Cohomogeneity One Manifolds Chenxu He Prof. Wolfgang Ziller, Advisor A Riemannian manifold M is called cohomogeneity one if it admits an isometric action by a compact Lie group G and the orbit space is one dimension. Many new examples of non-negatively curved manifolds were discovered recently in this category. However not every cohomogeneity one manifold carries an invari...

Almost Homogeneous Manifolds with Boundary

In this article we study the classification of some Lie group actions on differentiable manifolds, up to conjugacy. Let us start with the precise notion of conjugacy we shall use. Two C r actions ρ1, ρ2 of a Lie group G on a manifold M are said to be C r conjugate if there is a C r diffeomorphism Φ : M → M that is (ρ1, ρ2) equivariant, that is: Φ(ρ1(g)x) = ρ2(g)Φ(x) ∀x ∈ M ∀g ∈ G. A conjugacy c...