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March 2013 The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces
Minoru Tanaka, Kei Kondo
Nagoya Math. J. 209: 23-34 (March 2013). DOI: 10.1215/00277630-1959451

Abstract

We construct distinctive surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comparison theorems in radial curvature geometry. Moreover, we prove that a complete noncompact Riemannian manifold M is homeomorphic to the interior of a compact manifold with boundary if the manifold M is not less curved than a noncompact model surface of revolution and if the total curvature of the model surface is finite and less than 2π. By the first result mentioned above, the second result covers a much wider class of manifolds than that of complete noncompact Riemannian manifolds whose sectional curvatures are bounded from below by a constant.

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Minoru Tanaka. Kei Kondo. "The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces." Nagoya Math. J. 209 23 - 34, March 2013. https://doi.org/10.1215/00277630-1959451

Information

Published: March 2013
First available in Project Euclid: 27 February 2013

zbMATH: 1266.53041
MathSciNet: MR3032137
Digital Object Identifier: 10.1215/00277630-1959451

Subjects:
Primary: 53C21
Secondary: 53C22

Rights: Copyright © 2013 Editorial Board, Nagoya Mathematical Journal

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Vol.209 • March 2013
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