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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The total split curvatures of knotted space-like $2$-spheres in Minkowski $4$-space
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by Marek Kossowski PDF
Proc. Amer. Math. Soc. 117 (1993), 813-818 Request permission

Abstract:

In this paper we establish an analogue of the Fary-Milnor Theorem for space-like $2$-spheres in Minkowski $4$-space.
References
    E. Artin, Zur Isotopie Zweidimensionaler Flächen in ${{\mathbf {R}}^4}$, Abh. Math. Sem. Univ. Hamburg 4 (1925).
  • Marek Kossowski, The $S^2$-valued Gauss maps and split total curvature of a space-like codimension-$2$ surface in Minkowski space, J. London Math. Soc. (2) 40 (1989), no. 1, 179–192. MR 1028922, DOI 10.1112/jlms/s2-40.1.179
  • —, Fully stratified compact hypersurfaces in $4$-dimensional Minkowski space, preprint. —, The null blow up and intersection in the space like Grassmann for compact surfaces in Minkowski $3$-space, Michigan Math. J. 38 (1991).
  • J. W. Milnor, On the total curvature of knots, Ann. of Math. (2) 52 (1950), 248–257. MR 37509, DOI 10.2307/1969467
  • Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 813-818
  • MSC: Primary 53C50; Secondary 53C42, 57Q45
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1145420-1
  • MathSciNet review: 1145420