English

Differential geometry of spatial curves for gauges

Differential Geometry 2020-01-07 v1

Abstract

We derive Frenet-type results and invariants of spatial curves immersed in 33-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.

Keywords

Cite

@article{arxiv.2001.01379,
  title  = {Differential geometry of spatial curves for gauges},
  author = {Vitor Balestro and Horst Martini and Makoto Sakaki},
  journal= {arXiv preprint arXiv:2001.01379},
  year   = {2020}
}
R2 v1 2026-06-23T13:03:28.861Z