Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0606.53028
Cheeger, Jeff; Gromov, Mikhael
Collapsing Riemannian manifolds while keeping their curvature bounded. I. (English)
[J] J. Differ. Geom. 23, 309-346 (1986). ISSN 0022-040X

This is a very interesting paper of fundamental importance. It is the first of two papers devoted to the study of Riemannian manifolds with bounded curvature and (uniformly) "small" injectivity radius. Here it is shown that if a smooth manifold M admits a certain topological structure called an F-structure of positive rank (to be thought of as compatible partial actions by tori), then M also admits a family of Riemannian metrics, $g\sb{\delta}$, with uniformly bounded curvature, such that as $\delta\to 0$, the injectivity radius, $i\sb p$, converges uniformly to zero at all points, $p\in M$. The paper is enhanced by a number of illuminating examples. We are looking forward to the second part in which a sort of strengthened converse of the result indicated above is proved.
[K.Grove]

MSC 2000:: *53C20 Riemannian manifolds (global)

Keywords: collapse with bounded curvature; injectivity radius; F-structure of positive rank

Cited in: Zbl 1239.53052 Zbl 1261.53043 Zbl 1161.53026 Zbl 1155.53023 Zbl 1105.58013 Zbl 1098.57010 Zbl 1086.53050 Zbl 1081.53073 Zbl 1051.53034 Zbl 1049.53029 Zbl 0930.53040 Zbl 0813.53030 Zbl 0787.53030 Zbl 0791.53042 Zbl 0772.53028 Zbl 0722.53045 Zbl 0796.53048 Zbl 0727.53043 Zbl 0718.53038 Zbl 0716.53042 Zbl 0735.53033 Zbl 0676.58050

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]