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On the number of diffeomorphism classes in a certain class of Riemannian manifolds

Published online by Cambridge University Press:  22 January 2016

Takao Yamaguchi
Takao Yamaguchi*
Affiliation:
Saga University, Faculty of Science and Engineering, Saga 840, Japan
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The study of finiteness for Riemannian manifolds, which has been done originally by J. Cheeger [5] and A. Weinstein [13], is to investigate what bounds on the sizes of geometrical quantities imply finiteness of topological types, —e.g. homotopy types, homeomorphism or diffeomorphism classes-— of manifolds admitting metrics which satisfy the bounds. For a Riemannian manifold M we denote by RM and KM respectively the curvature tensor and the sectional curvature, by Vol (M) the volume, and by diam(M) the diameter.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 97 , March 1985 , pp. 173 - 192
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

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