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.
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