Mathematische Annalen

, Volume 277, Issue 1, pp 95–111 | Cite as

Submanifolds with flat normal bundle

  • Chuu-Lian Terng


Normal Bundle Flat Normal Bundle 
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  1. 1.
    Bishop, R.L., Crittenden, R.J.: Geometry of manifolds. New York: Academic Press 1964Google Scholar
  2. 2.
    Cairns, S., Morse, M.: Critical point theory in global analysis and differential topology. New York: Academic Press 1969Google Scholar
  3. 3.
    Cartan, É.: Leçons sur la géométrie des espaces de Riemann. Paris: Gauthier Villars 1946Google Scholar
  4. 4.
    Carter, S., West, A.: Tight and taut immersions. Proc. Lond. Math. Soc.25, 701–720 (1972)Google Scholar
  5. 5.
    Carter, S., West, A.: Isoparametric systems and transnormality. Proc. Lond. Math. Soc.51, 520–542 (1985)Google Scholar
  6. 6.
    Cecil, T.E.: Taut immersions of non-compact surfaces into a Euclidean 3-space. J. Differ. Geom.11, 451–459 (1976)Google Scholar
  7. 7.
    Cecil, T.E., Ryan, P.J.: Focal sets of submanifolds. Pac. J. Math.78, 27–39 (1978)Google Scholar
  8. 8.
    Cecil, T.E., Ryan, P.J.: Focal sets, taut embeddings and the cyclides of Dupin. Math. Ann.236, 177–190 (1978)Google Scholar
  9. 9.
    Cecil, T.E., Ryan, P.J.: Tight spherical embeddings. Lect. Notes Math.838, 94–104 (1981)Google Scholar
  10. 10.
    Cecil, T.E., Ryan, P.J.: Tight and taut immersions of manifolds, research notes in math. Vol. 107. Boston: Pitman 1985Google Scholar
  11. 11.
    Chern, S.S.: Minimal submanifolds in a Riemannian manifold. Notes of Univ. of KansasGoogle Scholar
  12. 12.
    Chern, S.S., Lashof, R.K.: On the total curvature of immersed manifolds I. Am. J. Math.79, 306–318 (1957); II. Mich. Math. J.5, 5–12 (1958)Google Scholar
  13. 13.
    De Almeida, S.C.: Minimal hypersurfaces ofS 4 with non-zero Gauss-Kronecker curvature. Bol. Soc. Bras. Mat.14, 137–146 (1983)Google Scholar
  14. 14.
    Eisenhart, L.P.: A treatise on the differential geometry of curves and surfaces. Boston: Ginn 1909Google Scholar
  15. 15.
    Hsiang, W.Y., Palais, R.S., Terng, C.L.: The topology and geometry of isoparametric submanifolds in Euclidean spaces. Proc. Natl. Acad. Sci. USA82, 4863–4865 (1985), full paper in preprint formGoogle Scholar
  16. 16.
    Kobayashi, S., Nomizu, K.: Foundations of differential geometry, I, II. New York: Interscience 1963Google Scholar
  17. 17.
    Kuiper, N.H.: Minimal total absolute curvature for immersions. Invent. Math.10, 209–238 (1970)Google Scholar
  18. 18.
    Lawson, H.B. Jr.: Complete minimal surfaces inS 3. Ann. Math. II. Ser.92, 335–374 (1970)Google Scholar
  19. 19.
    Lichnerowicz, A.: Géométrie des groupes de transformations. Paris: Dunod 1958Google Scholar
  20. 20.
    Milnor, J.W.: Morse theory. Ann. Math. Stud. 51. Princeton: University Press 1963Google Scholar
  21. 21.
    Miyaoka, R.: Compact Dupin hypersurfaces with three principal curvatures. Math. Z.187, 433–452 (1984)Google Scholar
  22. 22.
    Münzner, H.F.: Isoparametric Hyperflächen in Sphären, I, II. Math. Ann.251, 57–71 (1980);256, 215–232 (1981)Google Scholar
  23. 23.
    Nomizu, K.: Characteristic roots and vectors of a differentiable family of symmetric matrices. Linear Multilinear Algebra2, 159–162 (1973)Google Scholar
  24. 24.
    Nomizu, K.: Élie Cartan's work on isoparametric families of hypersurfaces. Proc. Symp. Pure Math.27, 191–200 (1975)Google Scholar
  25. 25.
    Nomizu, K., Rodriguez, L.L.: Umbilical submanifolds and Morse functions. Nagoya Math. J.48, 197–201 (1972)Google Scholar
  26. 26.
    O'Neill, B.: The fundamental equations of a submersion. Mich. Math. J.13, 459–469 (1966)Google Scholar
  27. 27.
    Pinkall, U.: Hypersurfaces of Dupin (preprint)Google Scholar
  28. 28.
    Pinkall, U.: Curvature properties of taut submanifolds (preprint)Google Scholar
  29. 29.
    Reckziegel, H.: On the eigenvalues of the shape operator of an isometric immersion into a space of constant curvature. Math. Ann.243, 71–82 (1979)Google Scholar
  30. 30.
    Thorbergsson, G.: Dupin hypersurfaces. Bull. Lond. Math. Soc.15, 493–498 (1983)Google Scholar
  31. 31.
    Thorbergsson, G.: Highly connected taut submanifolds. Math. Ann.265, 399–405 (1983)Google Scholar
  32. 32.
    Terng, C.-L.: Isoparametric submanifolds and their Coxeter groups. J. Differ. Geom.21, 79–107 (1985)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Chuu-Lian Terng
    • 1
  1. 1.Department of MathematicsNortheastern UniversityBostonUSA

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