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On the differential geometry of curves in Minkowski space

J. B. Formiga·C. Romero
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Abstract

We discuss some aspects of the differential geometry of curves in Minkowski space. We establish the Serret-Frenet equations in Minkowski space and use them to give a very simple proof of the fundamental theorem of curves in Minkowski space. We also state and prove two other theorems which represent Minkowskian versions of a very known theorem of the differential geometry of curves in tridimensional Euclidean space. We discuss the general solution for torsionless paths in Minkowki space. We then apply the four-dimensional Serret-Frenet equations to describe the motion of a charged test particle in a constant and uniform electromagnetic field and show how the curvature and the torsions of the four-dimensional path of the particle contain information on the electromagnetic field acting on the particle.

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J. B. Formiga, C. Romero. 2005-12-31. On the differential geometry of curves in Minkowski space. https://doi.org/10.1119/1.2232644

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