We study the dynamical breaking of chiral and color symmetries of dense quark
matter in the ultrastatic hyperbolic spacetime R⊗H3 in the framework
of an extended Nambu--Jona-Lasinio model. On the basis of analytical
expressions for chiral and color condensates as functions of curvature and
temperature, the phenomenon of dimensional reduction and gravitational
catalysis of symmetry breaking in strong gravitational field is demonstrated in
the regime of weak coupling constants. In the case of strong couplings it is
shown that curvature leads to small corrections to the flat-space values of
condensate and thus enhances the symmetry breaking effects. Finally, using
numerical calculations phase transitions under the influence of chemical
potential and negative curvature are considered and the phase portrait of the
system is constructed.Comment: 14 pages, 5 figure