Curvature types of planar curves for gauges

@article{Balestro2020CurvatureTO,
  title={Curvature types of planar curves for gauges},
  author={Vitor Balestro and Horst Martini and Makoto Sakaki},
  journal={Journal of Geometry},
  year={2020},
  volume={111},
  pages={1-12}
}
In this paper results from the differential geometry of curves are extended from normed planes to gauge planes which are obtained by neglecting the symmetry axiom. Based on the gauge analogue of the notion of Birkhoff orthogonality from Banach space theory, we study all curvature types of curves in gauge planes, thus generalizing their complete classification for normed planes. We show that (as in the subcase of normed planes) there are four such types, and we call them analogously Minkowski… 
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References

SHOWING 1-10 OF 10 REFERENCES
Classical curve theory in normed planes
Differential geometry of immersed surfaces in three-dimensional normed spaces
In this paper we study curvature types of immersed surfaces in three-dimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field
Surface immersions in normed spaces from the affine point of view
The aim of this paper is to investigate the differential geometry of immersed surfaces in three-dimensional normed spaces from the viewpoint of affine differential geometry. We endow the surface with
Antinorms and Radon curves
Summary.A Radon curve can be used as the unit circle of a norm, with the corresponding normed plane called a Radon plane. An antinorm is a special case of the Minkowski content of a measurable set in
An Introduction to Riemann-Finsler Geometry
One Finsler Manifolds and Their Curvature.- 1 Finsler Manifolds and the Fundamentals of Minkowski Norms.- 1.0 Physical Motivations.- 1.1 Finsler Structures: Definitions and Conventions.- 1.2 Two
Riemann-Finsler geometry
# Finsler Metrics # Structure Equations # Geodesics # Parallel Translations # S-Curvature # Riemann Curvature # Finsler Metrics of Scalar Flag Curvature # Projectively Flat Finsler Metrics
Pseudo-minkowski differential geometry
SummaryMinkowski geometry is studied by the method of moving frames.
Bi - and multifocal curves and surfaces for gauges
  • J . Convex Anal .
  • 1965