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Proceedings of the American Mathematical Society

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More on tight isometric immersions of codimension two


Author: Chang Shing Chen
Journal: Proc. Amer. Math. Soc. 40 (1973), 545-553
MSC: Primary 53C40
DOI: https://doi.org/10.1090/S0002-9939-1973-0375169-1
MathSciNet review: 0375169
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Abstract: We continue our investigation on tight isometric immersion of a nonnegatively curved compact manifold $ {M^n}$ into $ {R^{n + 2}}$. Under some minor restrictions, we prove that the immersion is a product embedding of convex hypersurfaces. For surfaces in $ {R^4}$, the restrictions are unnecessary.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0375169-1
Keywords: Tight isometric immersion, product embedding, curvature, top set, convex curves, flat torus
Article copyright: © Copyright 1973 American Mathematical Society