Type I Almost-Homogeneous Manifolds of Cohomogeneity One—IV

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∗

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...

Manifolds of Cohomogeneity Two

First, a word from our sponsor (particle physics). The mathematical reader should not expect to understand the physics, but (paraphrasing A. N. Varchenko) just let the words wash over you like music. Acharya & Witten [1] and Atiyah & Witten [2] have demonstrated that singularities in G2 holonomy manifolds 1 can compactify M -theory yielding effective quantum field theories in 3+1 dimensional Mi...

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...