2 papers
math.DG2024
A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form
Rafael López
We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface.…
math.DG2024
Differential geometry of curves in dual space
Rafael López
We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature…