3 papers
math.DG2025
A Complete Characterization of Pythagorean Hodograph Preserving Mappings
Amedeo Altavilla, Hans-Peter Schröcker, Zbyněk Šír +1
We fully characterize the mappings that send every Pythagorean-hodograph (PH) curve to a PH curve. We prove that in any dimension, such mappings are precisely the conformal fun…
math.DG2025
Lie Group Approach to Envelope Surfaces
Michal Molnár, Zbyněk Šír, Jana Vráblíková
In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces o…
math.CV2025
Minimal Surfaces via Complex Quaternions
Amedeo Altavilla, Hans-Peter Schröcker, Zbyněk Šír +1
Minimal surfaces play a fundamental role in differential geometry, with applications spanning physics, material science, and geometric design. In this paper, we explore a novel qua…