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Isothermal hypersurfaces and three-dimensional Dupin-Mannheim hypercyclides

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Literature cited

  1. J. A. Schouten, “Über die konforme Abbildung n-dimensionaler Mannigfaltigkeiten mit quadratischer Massbestimmung auf eine Mannigfaltigkeit mit euklidischer Massbestimmung,” Math. Z.,11, 58–88 (1921).

    Google Scholar 

  2. L. L. Verbitskii, “Geometry of conformally Euclidean spaces of class 1,” Tr. Sem. Vekt. Tenzorn. Analiz.,9, 146–182 (1952).

    Google Scholar 

  3. B.-Y. Chen and K. Yano, “Special conformally flat spaces and canal hypersurfaces,” Tokhoku Math. J.,25, No. 2, 177–184 (1973).

    Google Scholar 

  4. H. Shapiro, “Sur les éspaces sous-projectifs,” C. R. Acad. Sci.,191, 551–552 (1930).

    Google Scholar 

  5. G. I. Kruchkovich, “Spaces of V. F. Kagan,” in: Subprojective spaces [in Russian], V. F. Kagan (ed.), Moscow (1961), pp. 163–198.

  6. L. L. Verbitskii, “Hypersurfaces of three dimensions, realizing a conformally Euclidean metric,” Tr. Sem. Vekt. Tenzorn. Anailizu,12, 339–354 (1963).

    Google Scholar 

  7. A. Finzi, “Le ipersuperficie a tre dimensioni che si possono rapresentare conformente sullo spazio euclideo,” Atti Ist. Veneto,62, 1049–1062 (1902–1903).

    Google Scholar 

  8. G. M. Lancaster, “A characterization of certain conformally Euclidean spaces of class one,” Proc. Am. Math. Soc.,21, 623–628 (1969).

    Google Scholar 

  9. G. M. Lancaster, “Canonical metrics for certain conformally Euclidean spaces of dimension three and codimension one,” Duke Math. J.,40, 1–8 (1973).

    Google Scholar 

  10. T. Cecil and P. Ryan, “Focal sets, taut embeddings, and the cyclides of Dupin,” Math. Ann.,236, No. 2, 177–190 (1978).

    Google Scholar 

  11. R. Lilienthal, “Besondere Flächen,” in: Enz. Math. Wissensch. IIIB5 (1905), pp. 269–353.

    Google Scholar 

  12. H. Reckziegel, “Krümmungsflächen von isometrischen Immersionen in Räume konstanter Krümmung,” Math. Ann.,223, No. 2, 169–181 (1976).

    Google Scholar 

  13. G. Thorbergsson, “Dupin hypersurfaces,” Bull. London Math. Soc.,15, No. 5, 493–498 (1983).

    Google Scholar 

  14. R. Miyaoka, “Compact Dupin hypersurfaces with three principal curvatures,” Math. Z.,187, No. 4, 433–452 (1984).

    Google Scholar 

  15. U. Pinkall, “Dupin hypersurfaces,” Math. Ann.,270, No. 3, 427–440 (1985).

    Google Scholar 

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Authors and Affiliations

  1. Tartu State University, USSR

    M. E. Vyal'yas & Yu. G. Lumiste

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  1. M. E. Vyal'yas
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  2. Yu. G. Lumiste
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Translated from Matematicheskie Zametki, Vol. 41, No. 5, pp. 731–740, May, 1987.

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Vyal'yas, M.E., Lumiste, Y.G. Isothermal hypersurfaces and three-dimensional Dupin-Mannheim hypercyclides. Mathematical Notes of the Academy of Sciences of the USSR 41, 411–417 (1987). https://doi.org/10.1007/BF01159868

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  • DOI: https://doi.org/10.1007/BF01159868

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