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Focal sets, taut embeddings and the cyclides of Dupin

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References

  1. Banchoff, T.: The spherical two-piece property and tight surfaces in spheres. J. Differential Geometry4, 193–205 (1970)

    Google Scholar 

  2. Carter, S., West, A.: Tight and taut immersions. Proc. London Math. Soc.25, 701–720 (1972)

    Google Scholar 

  3. Cecil, T.: Taut immersions of non-compact surfaces into a Euclidean 3-space. J. Differential Geometry11, 451–459 (1976)

    Google Scholar 

  4. Cecil, T., Ryan, P.: Focal sets of submanifolds. (to appear in Pacific J. Math.)

  5. Dupin, C.: Applications de géométrie et de méchanique. Paris 1822

  6. Eisenhart, L.: A treatise on the differential geometry of curves and surfaces. Boston: Ginn 1909

    Google Scholar 

  7. Hirsch, M.: Differential topology. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  8. Klein, F.: Vorlesungen über höhere Geometrie, Third ed. New York: Chelsea 1957

    Google Scholar 

  9. Kobayashi, S., Nomizu, K.: Foundations of differential geometry, Vols. 1 and 2. New York: Wiley-Interscience 1963 and 1969

    Google Scholar 

  10. Kuiper, N.: On convex maps. Nieuw Arch. Wisk.10, 147–164 (1962)

    Google Scholar 

  11. Lilienthal, R.: Besondere Flächen. In: Encyklopädie der Math. Wissenschaften, Vol. III, 3, pp. 269–354. Leipzig: B. G. Teubner 1902–1927

    Google Scholar 

  12. Milnor, J.: Morse theory. Ann. of Math. Studies, No. 51. Princeton: Princeton University Press 1963

    Google Scholar 

  13. Morse, M., Cairns, S.: Critical point theory in global analysis and differential topology. New York: Academic Press 1969

    Google Scholar 

  14. Nomizu, K., Rodriguez, L.: Umbilical submanifolds and Morse functions. Nagoya Math. J.48, 197–201 (1972)

    Google Scholar 

  15. Palais, R.: A global formulation of the Lie theory of transformation groups. Mem. Amer. Math. Soc.22 (1957)

  16. Ryan, P.: Homogeneity and some curvature conditions for hypersurfaces. Tôhoku Math. J.21, 363–388 (1969)

    Google Scholar 

  17. Stoker, J.: Differential geometry. New York: Wiley-Interscience 1969

    Google Scholar 

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During the period of this research, the authors were supported by the following grants, T. E. Cecil, NSF Grant no. MCS76-07044, P. J. Ryan, NSF Grant no. MCS76-06930

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Cecil, T.E., Ryan, P.J. Focal sets, taut embeddings and the cyclides of Dupin. Math. Ann. 236, 177–190 (1978). https://doi.org/10.1007/BF01351390

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