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Sections of the light cone in Minkowski 4-space
Secciones del cono de luz en el espacio de Minkowski 4-dimensional
DOI:
https://doi.org/10.15446/recolma.v57n1.112371Palabras clave:
Minkowski 4-space, light cone, conic sections, hyperquadrics (en)Espacio de Minkowski 4-dimensional, cono de luz, secciones cónicas, hipercuádricas (es)
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The intersection of an affine hyperplane in L4 with the light cone C is called a conic section. In this paper, it is proved that the conic sections in L4 are either Riemannian spheres, hyperbolic spaces or horospheres, depending on the causal character of the hyperplane. Analogous results for affine sections of de Sitter and hyperbolic spaces in L4 are also presented at the end.
La intersección de un hiperplano afín en L4 con el cono de luz C se llama una sección cónica. En este artículo, probamos que las secciones cónicas de L4 son esferas de Riemann, espacios hiperbólicos o horoesferas, dependiendo del carácter causal del hiperplano. Al final del artículo presentamos resultados similares para secciones afines de espacios de Sitter y espacios hiperbólicos de L4.
Referencias
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