Geometry of Projective Planes over Two-Dimensional Algebras

Simple item page
dc.creatorAkivis, Maks A.
dc.creatorGoldberg, Vladislav V.
dc.date2000-10-19
dc.date.accessioned2026-07-07T06:33:17Z
dc.date.available2026-07-07T06:33:17Z
dc.descriptionThe authors study smooth lines on projective planes over the algebra C of complex numbers, the algebra C^1 of double numbers, and the algebra C^0 of dual numbers. In the space RP^5, to these smooth lines there correspond families of straight lines describing point three-dimensional tangentially degenerate submanifolds X^3 of rank 2. The authors study focal properties of these submanifolds and prove that they represent examples of different types of tangentially degenerate submanifolds. Namely, the submanifold X^3, corresponding in RP^5 to a smooth line γof the projective plane C, does not have real singular points, the submanifold X^3, corresponding in RP^5 to a smooth line γof the projective plane C^1 P^2, bears two plane singular lines, and finally the submanifold X^3, corresponding in RP^5 to a smooth line γof the projective plane C^0 P^2, bears one singular line.
dc.descriptionAMS-LaTeX, 11 pages
dc.identifierhttps://arxiv.org/abs/math/0010192
dc.identifierhttp://arxiv.org/abs/math/0010192
dc.identifierBeitraege Algebra Geom., 44 (2003) no. 1 165-178
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99145
dc.subjectDifferential Geometry
dc.subject53A20 (Primary), 14M99 (Secondary)
dc.titleGeometry of Projective Planes over Two-Dimensional Algebras
dc.typetext

Files

Collections

arXiv