We discuss and investigate the problem of existence of metric-compatible
linear connections for a given space-time metric which is, generally, assumed
to be semi-pseudo-Riemannian. We prove that under sufficiently general
conditions such connections exist iff the rank and signature of the metric are
constant. On this base we analyze possible changes of the space-time signature.Comment: 18 standard LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are
require