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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Curvature of product $3$-manifolds
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by James R. Wason PDF
Proc. Amer. Math. Soc. 72 (1978), 150-154 Request permission

Abstract:

Let M be a compact product 3-manifold without boundary. Let g be a Riemannian metric on M. If g has everywhere nonpositive sectional curvature, then g is locally diffeomorphic to a product metric. The proof is by the method of pseudoframes.
References
  • Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
  • Alexandre Preissmann, Quelques propriétés globales des espaces de Riemann, Comment. Math. Helv. 15 (1943), 175–216 (French). MR 10459, DOI 10.1007/BF02565638
    • J. R. Wason, Comparison of Riemannian structures by the method of pseudoframes, Thesis, Columbia Univ., 1973.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 72 (1978), 150-154
  • MSC: Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0503550-0
  • MathSciNet review: 503550