Codimension two nonorientable submanifolds with nonnegative curvature
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- by Yuriko Y. Baldin and Francesco Mercuri
- Proc. Amer. Math. Soc. 103 (1988), 918-920
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947682-8
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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
- Yuriko Y. Baldin and Francesco Mercuri, Isometric immersions in codimension two with nonnegative curvature, Math. Z. 173 (1980), no. 2, 111–117. MR 583380, DOI 10.1007/BF01159953
- J. P. Bourguignon and E. Mazet, Sur la structure des variétés riemanniennes qui admettent des champs de vecteurs parallèles, Compositio Math. 24 (1972), 105–117 (French). MR 307108
- C. Tompkins, A flat Klein bottle isometrically embedded in Euclidean 4-space, Bull. Amer. Math. Soc. 47 (1941), 508. MR 3976, DOI 10.1090/S0002-9904-1941-07501-4
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- 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