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Tautness and Lie sphere geometry

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References

  1. Arnold, V.: Mathematical methods of classical mechanics. Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  2. Blaschke, W.: Vorlesungen über Differentialgeometric, Vol. 3 Berlin: Springer 1929

    Google Scholar 

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

    Google Scholar 

  4. Cecil, T., Ryan, P.: Distance functions and umbilic submanifolds in hyperbolic space Nagoya Math. J.74, 67–75 (1979)

    Google Scholar 

  5. Cecil, T., Ryan, P.: Tight and taut immersions into hyperbolic space. J. London Math. Soc.19, 561–572 (1979)

    Google Scholar 

  6. Cecil, T., Ryan, P.: Tight spherical embeddings. Proc. 1979 Berlin Symposium in Global Differential Geometry. Lect. Notes Math.838, 94–104. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  7. Cecil, T., Ryan, P.: Tight and taut immersions of manifolds. Res. Notes Math.107, London: Pitman 1985

    Google Scholar 

  8. Hsiang, W.-Y., Palais, R., Terng, C.-L.: The topology of isoparametric submanifolds. Preprint, University of California, Berkeley 1986

    Google Scholar 

  9. Lie, S., Scheffers, G.: Geometrie der Berührungstransformationen. Leipzig:Teubner 1896

    Google Scholar 

  10. Ozawa, T.: On critical sets of distance functions to a taut submanifold. Math. Ann.276, 91–96 (1986)

    Google Scholar 

  11. Pinkall, U.: Dupin'sche Hyperflächen inE 4. Manuscr. Math.51, 89–119 (1985)

    Google Scholar 

  12. Pinkall, U.: Dupin hypersurfaces. Math. Ann.270, 427–440 (1985)

    Google Scholar 

  13. Pinkall, U.: Curvature properties of taut submanifolds. Geom. Dedicata20, 79–83 (1986)

    Google Scholar 

  14. Terng, C.-L.: Isoparametric submanifolds and their Coxeter groups. J. Differential Geometry21, 79–107 (1985)

    Google Scholar 

  15. Thorbergsson, G.: Dupin hypersurfaces. Bull. Lond. Math. Soc.15, 493–498 (1983)

    Google Scholar 

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Dedicated to Friedrich Hirzebruch on the occasion of his sixtieth birthday

This work was done while the author was on sabbatical at the University of California, Berkeley in 1985–86

Work done under support of NSF Grant No. DMS84-03201

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Cecil, T.E., Chern, SS. Tautness and Lie sphere geometry. Math. Ann. 278, 381–399 (1987). https://doi.org/10.1007/BF01458076

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