Dusek, Zdeněk Scalar invariants on special spaces of equiaffine connections. (English) Zbl 1206.53014 J. Lie Theory 20, No. 2, 295-309 (2010). The author firstly investigates invariants of torsionless connections with constant Christoffel symbols in \(\mathbb{R}^2\). For this aim, he calculates invariants of the corresponding representations of the group \(\text{SL}(2,\mathbb{R})\) on the space \(\mathbb{R}^6\) of Christoffel symbols. As a result, he finds three bi-quadratic polynomials forming a Hilbert basis of this representation. An interesting phenomenon (rational involutive maps of higher degree) appears during the calculation. The author also studies representations of \(\text{SL}(2,\mathbb{R})\) on the 9-dimensional space of special equiaffine connections in \(\mathbb{R}^3\) and corresponding invariants. Reviewer: R. Iordanescu (Bucureşti) MSC: 53A55 Differential invariants (local theory), geometric objects 53B05 Linear and affine connections 16R50 Other kinds of identities (generalized polynomial, rational, involution) 53A15 Affine differential geometry Keywords:equiaffine connection; representation of a Lie group; invariant function; Hilbert basis of invariants; involutive rational mapping × Cite Format Result Cite Review PDF Full Text: Link