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Ruled submanifolds with finite type Gauss map

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Abstract

We show that a ruled submanifold with finite type Gauss map in a Euclidean space is a cylinder on a curve of finite type or a plane.

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References

  1. BAIKOUSSIS, C., CHEN, B.-Y. and VERSTRAELÈN, L.: Ruled surfaces and tubes with finite type Gauss map, Tokyo J. Math.16 (1993), 341–349.

    Google Scholar 

  2. BARBOSA, J.M., DAJCZER, M. and JORGE, L.P.: Minimal ruled submamfolds in spaces of constant curvature, Indiana Univ. Math. J.33 (1984), 531–547.

    Google Scholar 

  3. BLAIR, D.E. and VANSTONE, J.R.: A generalization of the helicoid, “Minimal submanifolds and geodesics,” Kaigai Publications, Tokyo, 1978, 13–16.

    Google Scholar 

  4. CHEN, B.-Y.: Total mean curvature and submanifolds of finite type, World Scientific, Singapore, 1984.

    Google Scholar 

  5. CHEN, B.-Y.: Some open problems and conjectures on submanifolds of finite type, Soochow J. Math.17 (1991), 169–188.

    Google Scholar 

  6. CHEN, B.-Y., DILLEN, F., VERSTRAELEN, L. and VRANCKEN, L.: Ruled surfaces of finite type, Bull. Austral. Math. Soc.42 (1990), 447–453.

    Google Scholar 

  7. CHEN, B.-Y. and PICCINI, P.: Submanifolds with finite type Gauss map, Bull. Austral. Math. Soc.35 (1987), 161–186.

    Google Scholar 

  8. DILLEN, F.: Ruled submanifolds, Proc. Amer. Math. Soc.114 (1992), 795–798.

    Google Scholar 

  9. LUMISTE, U.: Die n-dimensional Minimalflächen mit einer (n−1)-dimensionalen asymptotischen Richtung in jedem Punkte, Tartu Riikl, Ül. Toimetised62 (1958), 117–141. (Russian, German summary.)

    Google Scholar 

  10. THAS, C.: Minimal generalized ruled surfaces in the Euclidean spaceE m, Internal Report Seminar of Higher Geometry, State University of Ghent.

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Dedicated to Professor N.K. Stephanidis on the occasion of his 65th birthday.

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Baikoussis, C. Ruled submanifolds with finite type Gauss map. J Geom 49, 42–45 (1994). https://doi.org/10.1007/BF01228047

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  • DOI: https://doi.org/10.1007/BF01228047

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