# 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…

## 3 Citations

Differential geometry of spatial curves for gauges

- MathematicsSão Paulo Journal of Mathematical Sciences
- 2020

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…

J an 2 02 0 Differential geometry of spatial curves for gauges

- Mathematics
- 2020

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…

Rotational surfaces in a $3$-dimensional normed space

- Mathematics
- 2021

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…

## References

SHOWING 1-10 OF 10 REFERENCES

Surface immersions in normed spaces from the affine point of view

- MathematicsGeometriae Dedicata
- 2018

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

- Mathematics
- 2006

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

- Mathematics
- 2000

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

- Mathematics
- 2005

# 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

- Philosophy
- 1965

SummaryMinkowski geometry is studied by the method of moving frames.

Differential geometry of immersed surfaces in three-dimensional normed spaces

- MathematicsAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg
- 2020

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…

Bi - and multifocal curves and surfaces for gauges

- J . Convex Anal .
- 1965