Differential geometry of spatial curves for gauges

@article{Balestro2020DifferentialGO,
  title={Differential geometry of spatial curves for gauges},
  author={Vitor Balestro and Horst Martini and Makoto Sakaki},
  journal={S{\~a}o Paulo Journal of Mathematical Sciences},
  year={2020},
  pages={1-14}
}
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. 
Rotational surfaces in a $3$-dimensional normed space
We study rotational surfaces with constant Minkowski Gaussian curvature and rotational surfaces with constant Minkowski mean curvature in a 3-dimensional normed space with rotationally symmetric

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