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Ruled surfaces of finite type in 3- dimensional minkowski space

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Abstract

We show that a ruled surface M in E1 3 is of finite type if and only if M is minimal, or M is a part of a circular cylinder, or M is a part of a hyperbolic cylinder, or M is an isoparametric surface with null rules. We also give a complete classification of isoparametric ruled surfaces with null rules.

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References

  1. B.Y. Chen, Total mean curvature and submanifolds of finite type, World Scientific, Singapore 1984.

    Book  MATH  Google Scholar 

  2. B.Y. Chen, Null 2-type surfaces in E3 are circular cylinders, Kodai Math. J.. 11 (1988), 295–299.

    Article  MathSciNet  MATH  Google Scholar 

  3. B.Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken, Ruled surfaces of finite type, Bull. Austral. Math. Soc. 42 (1990), 447–453.

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Dillen, Ruled submanifolds of finite type, Proc. Amer. Math. Soc. 114 (1992), 795–798.

    Article  MathSciNet  MATH  Google Scholar 

  5. F. Dillen, I. Van de Woestyne, L. Verstraelen, J. Walrave, Curves of finite type in Minkowski space, preprint.

  6. J. Hahn, Isoparametric hypersurfaces in the pseudo-Riemannian space forms, Math. Z. 187 (1984), 195–208.

    Article  MathSciNet  MATH  Google Scholar 

  7. O. Kobayashi, Maximal surfaces in the 3-dimensional Minkowski space L 3, Tokyo J. Math. 6 (1983).

  8. I. Van de Woestyne, Minimal surfaces of the 3-dimensional Minkowski space, Geometry and Topology of Submanifolds, II, World Scientific, Singapore, 1990, pp. 344–369.

    Google Scholar 

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Dedicated to Professor Katsumi Nomizu on the occasion of his seventieth birthday

Senior Research Assistant of the National Fund for Scientific Research (Belgium)

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Dillen, F., Verstraelen, L., Van de Woestyne, I. et al. Ruled surfaces of finite type in 3- dimensional minkowski space. Results. Math. 27, 250–255 (1995). https://doi.org/10.1007/BF03322830

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  • DOI: https://doi.org/10.1007/BF03322830

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