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.

DOI Code: 10.1285/i15900932v31n2p17

Keywords: arc-length ; curvature ; generalized space-time model ; generalized Minkowski space ; Minkowski product ; indefinite-inner product ; Riemann manifold ; semi-inner product ; semiindefinite inner product ; semi-Riemann manifold

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