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On submanifolds of Finite Chen type and of Restricted type

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References

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

  2. B.-Y. Chen, Finite type submanifolds and generalizations, University of Rome, Rome, 1985.

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  4. B.-Y. Chen, Surfaces of finite type in Euclidean 3- space, Bull. Soc. Math. Belq., Ser. B, 39 (1987), 243–254.

    MATH  Google Scholar 

  5. B.-Y. Chen, J. Deprez, F. Dillen, L. Verstraelen and L. Vrancken, Finite type curves, in: Geometry and Topology of Submanifolds, II, World Scientific Publishers, 1990, 76–100.

  6. B.-Y. Chen, F. Dillen and L. Verstraelen, Finite type space curves, Soochow J. Math., 12 (1986), 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  7. B.-Y. Chen and M. Petrovic, On spectral decomposition of immersions of finite type, Bull. Austral. Math. Soc., 44 (1991), 117–129.

    Article  MathSciNet  MATH  Google Scholar 

  8. 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 

  9. B.-Y. Chen and F. Dillen, Quadrics of finite type, J. Geometry, 38 (1990), 16–22.

    Article  MathSciNet  MATH  Google Scholar 

  10. B.-Y. Chen, F. Dillen, L. Verstraelen and L. Vrancken, Submanifolds of restricted type, Preprint Series, Dept. Math., Kath. Univ. Leuven, 3 (1991), 213–224.

    Google Scholar 

  11. J. Colpaert and L. Verstraelen, Classification of the closed affine curves of finite type, Preprint Series, Dept. Math., Kath. Univ. Leuven, 1 (1989), 125–149.

    Google Scholar 

  12. J. Deprez, F. Dillen and L. Vrancken, Finite type curves on quadrics, Chinese J. Math., 18 (1990), 95–121.

    MathSciNet  MATH  Google Scholar 

  13. F. Dillen, M. Petrovic, L. Verstraelen and L. Vrancken, Classification of curves of Chen type 2, in: Differential Geometry in honor of Radu Rosca, K. U. Leuven, 1990.

  14. F. Dillen, J. Pas and L. Verstraelen, On surfaces of finite type in Euclidean 3- space, Kodai Math. J., 13 (1990), 10–21.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Gluck, Higher curvatures for curves in Euclidean space, Amer. Math. Monthly, 73 (1966), 699–704.

    Article  MathSciNet  MATH  Google Scholar 

  16. F. Klein & S. Lie, Über diejenige ebenen Kurven welche durch ein geschlossenes System von einfach unendlich vielen vertauschbaren linearen Transformationen in sich übergehen, Math. Ann., 4 (1871), 50–84.

    Article  MathSciNet  MATH  Google Scholar 

  17. K. Nomizu, What is affine differential geometry? Proc. Diff. Geom., Münster, (1982), 42–43.

  18. K. Nomizu, On completeness in affine differential geometry, Geometriae Dedicata, 20 (1986), 43–49.

    Article  MathSciNet  MATH  Google Scholar 

  19. K. Nomizu, A survey of recent results in affine differential geometry, Geometry and Topology of Submanifolds, III (1991), World Scientific Publisher, 227-256.

  20. T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan, 18 (1968), 203–215.

    Google Scholar 

  21. M. Petrovic, L. Verstraelen and L. Vrancken, 3 -type curves on ellipsoids of revolution, Preprint Series, Dept. Math., Kath. Univ. Leuven, 1 (1990), 31–49.

    Google Scholar 

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Verstraelen, L. On submanifolds of Finite Chen type and of Restricted type. Results. Math. 20, 744–755 (1991). https://doi.org/10.1007/BF03323208

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