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Normal congruences with focal bicylindrical surfaces

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Ukrainian Mathematical Journal Aims and scope

Abstract

A system of equations determining normal congruences with focal surfaces (bicylinders) is found in a biaxial space of hyperbolic type by using a moving frame of the space and the method of Cartan exterior forms. The geometric construction of these congruences is presented.

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References

  1. N. P. Koneva,Normal Congruences in a Biaxial Space of Hyperbolic Type [in Russian], Preprint No. 83.49, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1983).

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  2. N. P. Koneva, “Two propositions on congruences of biaxial space,”Ukr. Mat. Zh.,41, No. 11, 1471–1476 (1989).

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  3. S. P. Finikov,Theory of Congruences [in Russian], Gostekhizdat, Moscow (1956).

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  4. A. P. Norden, “The space of a linear congruence,”Mat. Sb.,24, No. 3, 429–455 (1949).

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Authors and Affiliations

  1. Kiev Polytechnic Institute, Kiev

    N. P. Koneva

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  1. N. P. Koneva
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 718–720, May, 1993.

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Koneva, N.P. Normal congruences with focal bicylindrical surfaces. Ukr Math J 45, 790–793 (1993). https://doi.org/10.1007/BF01058214

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  • DOI: https://doi.org/10.1007/BF01058214

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