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The equivalence of curves in \(SL(n,\mathbb R)\) and its application to ruled surfaces. (English) Zbl 1228.53014
Summary: The generating system of the differential algebra for invariant differential polynomials with two parametric curves is obtained. Conditions for the equivalence of two families of parametric curves are given. We also prove that the generating differential invariants of two parametric curves are independent. Finally, we reduce the \(SL(n,\mathbb R)\)-equivalent problem for ruled surfaces to that of parametric curves.

MSC:
53A55 Differential invariants (local theory), geometric objects
53A15 Affine differential geometry
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