Rectas proyectivas sobre R_álgebras bidimensionales y cuádricas en el espacio proyectivo
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Santiago Mazuelas Franco [1]
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[1] Universidad de Valladolid
Universidad de Valladolid
Valladolid, España
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- Localización: Boletín de la Sociedad Puig Adam de profesores de matemáticas, ISSN 1135-0261, Nº. 80, 2008, págs. 57-76
- Idioma: español
- Texto completo no disponible (Saber más ...)
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Resumen
The classic Riemann Sphere construction, that is, the real plane compactification by means of a sphere or equivalently via the complex projective line; is widely known and used. This construction achieves, for example, a clear description of cycles and a linear representation of the inversive group of the euclidean plane by means of the Moebius group. In this paper we study the analog construction for the other types of bidimensional ]_algebras: paracomplex and dual numbers, and for the other types of real and irreducible quadrics in the projective space: hyperboloid and real cone. We make a especial emphasis in the definition of the projective lines over rings with zero divisors. Thereby we show that it is possible to perform a construction com-pletely analogous to the Riemann Sphere for the other types of bidimen-sional algebras and quadrics in the projective space and we also show the relation of these constructions with the hyperbolic and degenerate metrics of the real plane.
