2013-№4(41) Article 16

O.V. Zacepina

Classification of hypercomplexes of lines in the frame in first order. p. 175-185.

UDC  514

In Lobachevskian geometry semiparametric complexes of lines are called hypercomplexes of lines. Hypercomplexes of lines are investigated by Elie Cartan’s method of external forms. The paper specifies hypercomplex vectors and provides a geometric interpretation of their choice. The paper deals with intrinsic and ideal hypercomplexes of lines, constant scalar curvature, degenerated hypercomplexes of lines.

hypercomplexes of lines in Lobachevskian five-dimensional space, linear differential forms, Elie Cartan’s external forms, first order neighborhood.

References

1.      Grincevichyus K.I. Differencialnaya okrestnost vtorogo poryadka lucha kompleksa v mnogomernom proektivnom prostranstve [Second-order differential neighborhood of a ray in the complex multi-dimensional projective space]. Litovsk. Math. Coll. – 1960 – v. 52 – no. 4 – pp. 991-1020.

2.      Zacepina O.V. Inflekcionno-metricheskij kompleks pryamyx v chetyryoxmernom prostranstve Lobachevskogo [Inflection-metric complex of lines in four-dimensional Lobachevsky]. Vestnik Rjazanskogo gosudarstvennogo universiteta imeni S. A. Esenina – Bulletin of the Ryazan State University named after S.A. Yesenin. – 2005 (I). – pp. 91-98.

3.      Kiotina G.V., Zacepina O.V., Zhmurova N.V. Kompleksy pryamyx v prostranstvax E32, Ap30, 1S3 [Complexes of lines in the spaces E32, Ap30, 1S3] // Geometriya v celom. Prepodavanie geometrii v VUZe i shkole. Materialy vserossijskoj nauchno-metodicheskoj konferencii Velikij Novgorod. – Geometry as a whole. Teaching geometry in high school and high school. All-Russian Scientific Conference Veliky Novgorod, 2004.

4.      Kiotina G.V. Klassifikaciya kompleksov pryamyx v repere pervogo poryadka v prostranstve E32 [Classification of complexes of lines in the frame first order in the space E32] // Izvestiya Saratovskogo universiteta. –  Herald of the University of Saratov, Vol.11, 2011.

5.      Kiotina G.V. Kompleksy pryamyx v biflagovom prostranstve. [Biflagovom complexes of lines in space].  / Vestnik Rjazanskogo gosudarstvennogo universiteta imeni S. A. Esenina – Bulletin of the Ryazan State University named after SA Yesenin. no. 35, 2012

6.      Rozenfeld B.A. , O.V. Zacepina, P.G. Steganceva Giperkompleksy pryamyx v evklidovom i neevklidovyx prostranstvax [Hypercomplexes of lines in Euclidean and non-Euclidean spaces]. // Izvestiya vuzov. Matematika. – Proceedings of the universities. Mathematics. – 1990. – no 3. – pp. 57–66