A remark on the Gromov convergence theorem

Author:
Yukio Otsu

Journal:
Proc. Amer. Math. Soc. **108** (1990), 491-494

MSC:
Primary 53C20

DOI:
https://doi.org/10.1090/S0002-9939-1990-0990431-7

MathSciNet review:
990431

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Abstract: In [3] M. Gromov introduced the concept of convergence of Riemannian manifolds and he proved the convergence theorem. Since that time the theorem has been developed in detail (see [5], [7], [2]), and we know that it contains some interesting applications. Nevertheless there seems to be an inadequate way of applying the convergence theorem. The purpose of this paper is to present an example which shows that it is not correct.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-0990431-7

Keywords:
Convergence theorem,
Pinching problem

Article copyright:
© Copyright 1990
American Mathematical Society