3 papers
math.DG2026
Quadric surfaces of revolution in the 3-sphere as cubic Weingarten surfaces
Ildefonso Castro, Daniel López-López
The study of quadric surfaces of revolution is a cornerstone of classical Euclidean geometry, but its extension to the three-dimensional sphere has not been sufficie…
math.DG2025
Isometric immersions into three-dimensional unimodular metric Lie groups
Ildefonso Castro, José M. Manzano, José S. Santiago
We study isometric immersions of surfaces into simply connected 3-dimensional unimodular Lie groups endowed with either Riemannian or Lorentzian left-invariant metrics, assuming th…
math.DG2024
Helicoidal minimal surfaces in the 3-sphere: An approach via spherical curves
Ildefonso Castro, Ildefonso Castro-Infantes, Jesús Castro-Infantes
We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous fun…