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Differential geometry of spatial curves for gauges

We derive Frenet-type results and invariants of spatial curves immersed in $3$-dimensional generalized Minkowski spaces, i.e., in linear spaces which satisfy all axioms of finite dimensional real Banach spaces except for the symmetry axiom. Further on, we characterize cylindrical helices and rectifying curves in such spaces, and the computation of invariants is discussed, too. Finally, we study how translations of unit spheres influence invariants of spatial curves.

preprint2020arXivOpen access
Vitor BalestroHorst MartiniMakoto Sakaki
math.DG
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Open access3 authors1 topic
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Vitor BalestroHorst MartiniMakoto Sakaki

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