The lightcone Gauss map and the lightcone developable of a spacelike curve in Minkowski 3-space. (English) Zbl 0970.53015

The authors define the notion of lightcone Gauss map, lightcone pedal curves and lightcone developables of spacelike curves in Minkowski 3-space. The Frenet-Serret type formulae play an essential role in these concepts. Two pairs of conditions formulated in the paper allow to define two sets of curves. One of them is residual in the set of spacelike curves equipped with the Whitney \(C^\infty\)-topology, the other one is residual in the set of spacelike curves with non-vanishing curvature. Geometric invariants of curves under the action of the Lorentz group are considered.


53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53A04 Curves in Euclidean and related spaces
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