𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Lower curvature bounds and cohomogeneity one manifolds

✍ Scribed by Lorenz J. Schwachhöfer

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
186 KB
Volume
17
Category
Article
ISSN
0926-2245

No coin nor oath required. For personal study only.

✦ Synopsis

We shall discuss Riemannian metrics of fixed diameter and controlled lower curvature bound. As in [34], we give a general construction of invariant metrics on homogeneous vector bundles of cohomogeneity one, which implies, in particular, that any cohomogeneity one manifold admits invariant metrics of almost nonnegative sectional curvature. This provides positive evidence for a conjecture by Grove and Ziller [24] which states that any cohomogeneity one manifold should have invariant metrics of nonnegative curvature.

📜 SIMILAR VOLUMES

Some topological properties of cohomogen
Some topological properties of cohomogeneity one manifolds with negative curvature
✍ Fabio Podestà; Andrea Spiro 📂 Article 📅 1996 🏛 Springer 🌐 English ⚖ 608 KB

This paper is aimed at studying negatively curved Riemannian manifolds acted on by a Lie group of isometries with principal orbits of codimension one. The orbit space of such a manifold M is proved to be always homeomorphic to R or R+ and this second case may occur only when either the singular orbi

Cohomogeneity one Riemannian manifolds a
Cohomogeneity one Riemannian manifolds and Killing fields
✍ Fabio Podestà 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 557 KB

This paper is devoted to the study of isometries of cohomogeneity one Riemannian spaces, namely Riemannian manifolds acted on by a Lie group of isometries G with principal ort';ts of codimension one. We show that, for a class of such manifolds, every one parameter group of isometrics preserves the f

RETRACTED: Cohomogeneity One Manifolds o
RETRACTED: Cohomogeneity One Manifolds of Spin(7) and G2 Holonomy
✍ M. Cvetič; G.W. Gibbons; H. Lu; C.N. Pope 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 327 KB

In this paper, we look for metrics of cohomogeneity one in D = 8 and D = 7 dimensions with Spin(7) and G 2 holonomy, respectively. In D = 8, we first consider the case of principal orbits that are S 7 , viewed as an S 3 bundle over S 4 with triaxial squashing of the S 3 fibres. This gives a more gen