2010/06/04 by Ákos G. Horváth, Horváth, Ákos G.
Mathematics · #46C20 #46C50 #53B40 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:46C20 #msc:46C50 #msc:53B40
paper · pdf · doi:10.48550/arxiv.1006.0857
35 pages
arxiv created 2010/06/04 · arxiv updated 2010/06/07
The tangent hyperplanes of the "manifolds" of this paper equipped a so-called Minkowski product. It is neither symmetric nor bilinear. We give a method to handing such an object as a locally hypersurface of a generalized space-time model and define the main tools of its differential geometry: its fundamental forms, its curvatures and so on. In the case, when the fixed space-time component of the embedding structure is a continuously differentiable semi-inner product space, we get a natural generalization of some important semi-Riemann manifolds as the hyperbolic space, the de Sitter sphere and the light cone of a Minkowski-Lorenz space, respectively.