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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.

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

References

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