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Stratifiable pairs of line complexes immersed in an elliptic spaceS 3

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Abstract

The present work is concerned mainly with the study of two kinds of stratifiable pairs of line complexes embedded in an elliptic spaceS 3 as a continuation of [1] and [6], For both kinds, examples and some geometrical properties are given. Our study is carried out using Cartan's method of moving frames ([3], [8]).

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References

  1. N. Dadažanov, Cikličeskie paryT n kompleksov (Cyclic pairs ofT n complexes),Sibirsk. Mat. Ž. 5 (1964), 793–803.MR 29 # 3971

    MathSciNet  MATH  Google Scholar 

  2. K. I. Duničev, Rasslojaemye pary paraboličeskih psevdokongruèncii prjamyh v četypehmernom proektivnom prostranstve (Stratifiable pairs of parabolic pseudocongruences of lines in a four-dimensional projective space),Moskov. Gos. Ped. Inst. Učen. Zap. 374/1 (1970), 81–86.MR 58 # 30794

    Google Scholar 

  3. S. P. Finikov, Metod vnešnih form Kartana v differencial'noi (Cartan's method of exterior forms in differential geometry), OGIZ, Moskva, 1948.MR 11—597

    Google Scholar 

  4. K. I. Grincevičjus (Grincevičius), Ob odnoi zadače par kompleksov (A problem on pairs of complexes),Litovsk. Mat. Sb. 4 (1964), 37–40.MR 29 # 6404

    MathSciNet  Google Scholar 

  5. M. T. Kovancov,Teorija kompleksov (Theory of complexes), Izdat. Kiev. Univ., Kiev, 1963.MR 33 # 4816

    Google Scholar 

  6. L. I. Magazinnikov andG. I. Ivanov, K. voprosu o centroaffinnon rassloenii par negolonomnyh kongruèncii pary kompleksov (On the question of the centroaffine stratification of pairs on nonholonomic congruences of a pair of complexes),Trudy Tomsk. Gos. Univ. 235 (1973), 150–164,MR 51 # 4075

    MathSciNet  Google Scholar 

  7. L. Rédei,Foundation of Euclidean and non-Euclidean geometries according to F. Klein, Akadémiai Kiadó, Budapest, 1968.MR 36 # 7005

    MATH  Google Scholar 

  8. W. Ślebodziński,Exterior forms and their applications, PWN, Warszawa, 1970.MR 42 # 6742

    MATH  Google Scholar 

  9. M. A. Soliman, Some geometrical properties of a moving frame conjugate to manifolds of lines in elliptic spaceS 3,Proc. Fifth Annual Conf. on Statistics, Computer Science, Operation Research, Cairo University, Cairo,15/5, 1980; 377–387.

    Google Scholar 

  10. M. A. Soliman andN. H. Abdel-All, Complexes of lines inS 3 with one of the principal surfaces coincident with the coordinate surface,Bull. Calcutta Math. Soc. (To appear)

  11. A. Švec,Projective differential geometry of line congruences, Publ. House Czechoslovak Acad. Sci., Praha, 1965.MR 33 # 7949

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science, Assiut University, Assiut, Egypt

    M. A. Soliman & N. H. Abdel-All

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  1. M. A. Soliman
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  2. N. H. Abdel-All
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Soliman, M.A., Abdel-All, N.H. Stratifiable pairs of line complexes immersed in an elliptic spaceS 3 . Period Math Hung 14, 155–161 (1983). https://doi.org/10.1007/BF01855427

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