Painlevé Expansions, Cohomogeneity One Metrics and Exceptional Holonomy

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∗

M theory and Singularities of Exceptional Holonomy Manifolds

M theory compactifications on G2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our underst...

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...