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Curves in affine and semi-Euclidean spaces. (English) Zbl 1330.53017

The author introduces the centroaffine invariants for curves in the centroaffine 2-dimensional and 3-dimensional spaces. Like in the Euclidean case such curves are determined by 1 curvature function in the 2-dimensional case, and 2 curvature functions in the 3-dimensional case.
As applications, amongst others, the curves with constant curvature functions, or the curves for which the affine arc length corresponds to the Euclidean arc length are classified.

MSC:

53A15 Affine differential geometry
53A04 Curves in Euclidean and related spaces
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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