  Real-valued triplet of scalar fields as source gives rise to a metric which
tilts the scalar, not the light cone, in 2+1-dimensions. The topological metric
is static, regular and it is characterized by an integer $\kappa =\pm 1,\pm
2,...$. The problem is formulated as a harmonic map of Riemannian manifolds in
which the integer $\kappa $ equals to the degree of the map.
