Premanifolds

Abstract

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.