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2-families of lines in P3 and pairs of congruent lines in P3

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Literature Cited

  1. B. A. Rozenfel'd, Metric Method in Projective Differential Geometry and Its Conformal and Contact Analogs, Matem. Sb.22, 457–492 (1948).

    Google Scholar 

  2. S. P. Finikov, Theory of Congruent Pairs [in Russian], GITTL, Moscow-Leningrad (1956).

    Google Scholar 

  3. E. T. Ivlev, Canonical Frame of Congruent Pairs in P3. Trudy Tomsk Univ, Geometrical Collection,160, 1, 15–24 (1962).

    Google Scholar 

  4. E. T. Ivlev, A Pair of Ruled Surfaces in P3, Trudy Tomsk Univ., Geometrical Collection,161, 2, 3–10 (1962).

    Google Scholar 

  5. S. E. Karapetyan, Projective Differential Geometry of Families of Multidimensional Planes, II, Izv. Akad. Nauk ArmSSR, Ser. Fiz.-matem.,16, No. 5, 2–22 (1963).

    Google Scholar 

  6. S. E. Karapetyan, Projective Differential Geometry of Two-Parameter Families of Lines and Planes in Four-Dimensional Projective Space, I, Izv. Akad. Nauk ArmSSR, Ser. Fiz.-matem.,15, No. 2, 25–43 (1962).

    Google Scholar 

  7. S. E. Karapetyan, The Pair A and Some Properties of the Pair T, Izv. Akad. Nauk ArmSSR. Ser. Fiz.-matem.,12, No. 4, 27–34 (1959).

    Google Scholar 

  8. S. E. Karapetyan, Conjugate Manifolds and Their Applications, Doklady Akad. Nauk SSSR,133, No. 5, 1007–1011 (1960).

    Google Scholar 

  9. S. E. Karapetyan, The Theory of Congruent Pairs, Izd. Akad, Nauk ArmSSR. Ser. Fiz.-matem.,14, No. 4, 37–47, (1961).

    Google Scholar 

  10. R. M. Geidel'man, Problems of Differential Geometry of Homogeneous Spaces, Trudy Moscow Inst. Inzh. Transporta, Questions of Differential Geometry,190, 5–20 (1965).

    Google Scholar 

  11. L. Z. Kruglyakov, Canonical Frame of a Nonfocal Two-Parameter Family of Lines in Five-Dimensional Projective Space, Trudy Tomsk Univ., Geometrical Collection,191, 6, 36–47, (1967).

    Google Scholar 

  12. G. P. Bochillo, On the Two-Parameter Manifold V2 of Semi-Noneuclidean Spaces in P4. Trudy Tomsk Univ., Geometrical Collection,191, 6, 23–31, (1967).

    Google Scholar 

  13. G. N. Makeev. Focal Congruent Pairs T and θ [in Russian], Transactions of the First Scientific Conference of the Mathematical Departments of the Povolzh'ya Pedagogic Institutes (1961). pp. 122–127.

  14. R. M. Geidel'man, The Tangent Linear Complex of a Congruent Pair of Lines, Izv. Vyssh. Uchebn. Zaved. Matem., No. 3, 32–38 (1966).

    Google Scholar 

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 9, No. 3, pp. 554–567, May–June, 1968.

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Kruglyakov, I.Z. 2-families of lines in P3 and pairs of congruent lines in P3 . Sib Math J 9, 417–426 (1968). https://doi.org/10.1007/BF01040904

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  • DOI: https://doi.org/10.1007/BF01040904

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