Collapsing and Almost Nonnegative Curvature

Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 17)

Abstract

Almost nonnegatively curved manifolds are charming spaces for at least two reasons: From a classical point of view, they are natural generalizations of almost flat as well as nonnegatively and positively curved manifolds, and the study of all of the latter has a long tradition in Riemannian geometry. Secondly, almost nonnegatively curved manifolds are precisely the spaces which can be collapsed to a point under a fixed lower bound on sectional curvature, so that in degenerations and convergence of metrics under lower curvature bounds they play the same fundamental role that almost flat manifolds do in Cheeger–Fukaya–Gromov’s theory of collapse with curvature bounded in absolute value.

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Fakultät für Mathematik Karlsruher Institut für Technologie (KIT)KarlsruheGermany

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