Speaker
Description
A generalized helix is a space curve whose tangent vectors make a constant angle with a fixed straight line, called the axis of a generalized helix. Among such curves, the ones that lay on a sphere show interesting geometric properties.
In Euclidean space, spherical generalized helices have a property that their orthogonal projections onto a plane normal to their axis appear as epicycloids, what contributes to the widespread of epicycloids in physics, as well as in robotics. Therefore, we were motivated to consider spherical generalized helices in 3-dimensional Lorentz-Minkowski space, the ambient space for general relativity theory.
We provide their characterizations in terms of curvature and torsion and analyze their projections onto planes orthogonal to their axes.
These projections appear as Euclidean or Lorentzian cycloidal curves, so we also introduce natural equations and parametrizations of Lorentzian cycloidal curves.
