On the number of diffeomorphism classes in a certain class of Riemannian manifolds. (English) Zbl 0566.53038

Yamaguchi, Takao

Nagoya Math. J. 97, 173-192 (1985).

Cheeger’s finiteness theorem asserts that there are only finitely many diffeomorphism classes in the class of compact Riemannian manifolds M of dimension n, such that the curvature of M is between two given bounds - \(\Lambda\) \({}^ 2_ 1\) and \(+ \Lambda^ 2_ 2\) and diameter(M)\(\leq D\), volume(M)\(\geq V\), where D and V are given. Extensions of this result to complete manifolds are discussed.

Reviewer: W.Ballmann

MSC:

53C20	Global Riemannian geometry, including pinching
57R55	Differentiable structures in differential topology

Keywords:

Cheeger’s finiteness theorem; diameter; volume; complete manifolds

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