Differential geometry of spatial curves for gauges

  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},
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
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Curvature types of planar curves for gauges
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Surface immersions in normed spaces from the affine point of view
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The geometry of Minkowski spaces — A survey. Part I
Riemann-Finsler geometry
# Finsler Metrics # Structure Equations # Geodesics # Parallel Translations # S-Curvature # Riemann Curvature # Finsler Metrics of Scalar Flag Curvature # Projectively Flat Finsler Metrics
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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
When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane?
3. S. Thomson, Real Analysis, Prentice Hall, Upper Saddle River, NJ, 1997.
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. 23
  • 2016