  More then forty years ago R.I. Pimenov introduced a new geometry --
semi-Riemannian one -- as a set of geometrical objects consistent with a
fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to
which the physically different quantities (meter, second, coulomb etc.) are
geometrically modelled as space coordinates that are not superposed by
automorphisms. As there is only one type of coordinates in Riemannian geometry
and only three types of coordinates in pseudo-Riemannian one, a multiple
fibered semi-Riemannian geometry is the most appropriate one for the treatment
of more then three different physical quantities as unified geometrical field
theory.
  Semi-Euclidean geometry $^{3}R_5^4$ with 1-dimensional fiber $x^5$ and
4-dimensional Minkowski space-time as a base is naturally interpreted as
classical electrodynamics. Semi-Riemannian geometry $^{3}V_5^4$ with the
general relativity pseudo-Riemannian space-time $^{3}V^4,$ and 1-dimensional
fiber $x^5,$ responsible for the electromagnetism, provides the unified field
theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where
the 5-th coordinate appears in nondegenerate Riemannian or pseudo-Riemannian
geometry, the theory based on semi-Riemannian geometry is free from defects of
the former. In particular, scalar field does not arise.
  PACS: 04.50.Cd, 02.40.-k, 11.10.Kk
