Collapsing and Almost Nonnegative Curvature

Conference paper

DOI: 10.1007/978-3-642-22842-1_4

Part of the Springer Proceedings in Mathematics book series (PROM, volume 17)
Cite this paper as:
Tuschmann W. (2012) Collapsing and Almost Nonnegative Curvature. In: Bär C., Lohkamp J., Schwarz M. (eds) Global Differential Geometry. Springer Proceedings in Mathematics, vol 17. Springer, Berlin, Heidelberg

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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