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Proceedings of the American Mathematical Society

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

 
 

 

Curvature of product $ 3$-manifolds


Author: James R. Wason
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
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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 [Enhancements On Off] (What's this?)

  • [1] S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. I, Interscience, New York, 1963. MR 0152974 (27:2945)
  • [2] A. Preissmann, Quelques propriétés des espaces de Riemann, Comment. Math. Helv. 15 (1942), 175-216. MR 0010459 (6:20g)
  • [3] J. R. Wason, Comparison of Riemannian structures by the method of pseudoframes, Thesis, Columbia Univ., 1973.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0503550-0
Keywords: Manifold, Riemannian metric, sectional curvature, pseudoframe
Article copyright: © Copyright 1978 American Mathematical Society

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