The only basic scalar invariant in the general equiaffine geometry is the determinant of the Ricci tensor.For special equiaffine geometries, more scalar invariants can emerge.In this paper, we first investigate invariants of torsion-less connections with constant Christoffel symbols in R 2 .For this aim, we calculate invariants of the corresponding representation of the group SL(2, R) on the space R 6 of Christoffel symbols.As a result, we find three bi-quadratic polynomials forming a Hilbert basis of this representation.An interesting phenomenon (rational involutive maps of higher degree) appears during the calculation.We also study representation of SL(2, R) on the 9-dimensional space of special equiaffine connections in R 3 and corresponding invariants.
Z. Dusek (Fri,) studied this question.