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Euler-Savary’s formula on Minkowski geometry. (English) Zbl 1066.53039

If in the Euclidean plane a curve \(c_R\) rolls without gliding along another curve \(c_B\), any point \(P\) attached to \(c_B\) runs on a path \(c_L\). The classical formula of Euler-Savary links the curvatures \(k_B\), \(k_R\) and \(k_L\) of the curves \(c_B\), \(c_R\) and \(c_L\). In this paper Euler-Savary’s formula is derived in case the underlying metric being Minkowskian instead of Euclidean.

MSC:

53A35 Non-Euclidean differential geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53A17 Differential geometric aspects in kinematics
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