**BPS-monopoles is 3-spaces of Euclide, Riemann, Lobachevsky**

**Abstract:**

Procedure of finding of the Bogomolny - Prasad - Sommerfield monopole
solutions
in the Georgi - Glashow model is investigated in detail on the backgrounds
of three space models of constant curvature: Euclid, Riemann, Lobachevsky.
Classification of possible solutions is given. It is shown that among
all solutions
there exist just three ones which reasonably and in a one-to-one
correspondence
can be associated with respective geometries. It is pointed out that the
known
non-singular BPS-solution in the flat Minkowski space can be understood
as a result
of somewhat artificial combining the Minkowski space background with a
possibility
naturally linked up with the Lobachewsky geometry. The standpoint is
brought forth
that of primary interest should be regarded only three specifically
distinctive
solutions - one for every curved space background. In the framework of those
arguments the generally accepted status of the known monopole BPS-solution
should be critically reconsidered and even might be given away.

Joint work with S.Yu. Sakovich (B.I. Stepanov Institute of Physics, Minsk, Belarus).