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Codimension two nonorientable submanifolds with nonnegative curvature


Authors: Yuriko Y. Baldin and Francesco Mercuri
Journal: Proc. Amer. Math. Soc. 103 (1988), 918-920
MSC: Primary 53C40
DOI: https://doi.org/10.1090/S0002-9939-1988-0947682-8
MathSciNet review: 947682
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Abstract: We prove that a compact nonorientable $ n$-dimensional submanifold of $ {{\mathbf{R}}^{n + 2}}$ with nonnegative curvature is a "generalized Klein bottle" if $ n \geq 3$.


References [Enhancements On Off] (What's this?)

  • [1] Y. Y. Baldin and F. Mercuri, Isometric immersions in codimension two with nonnegative curvature, Math. Z. 173 (1980), 111-117. MR 583380 (83c:53061)
  • [2] J. P. Bourguignon and E. Mazet, Sur la structure des variétés riemanniennes qui admettent des champs de vecteurs paralleles, Compositio Math. 24 (1972), 105-117. MR 0307108 (46:6229)
  • [3] C. Tompkins, A flat Klein bottle isometrically imbedded in Euclidean $ 4$-space, Bull. Amer. Math. Soc. 47 (1941), 508. MR 0003976 (2:301d)

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DOI: https://doi.org/10.1090/S0002-9939-1988-0947682-8
Article copyright: © Copyright 1988 American Mathematical Society

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