ANALYSIS OF GEODESICS ON DIFFERENT SURFACES - Maksimović, Miroslav; Jovanović, Tanja; Ljajko, Eugen; Ivanović, Milica (Bulletin of Natural Sciences Research, 2020)
It is widely known that some surfaces contain special curves as a geodesics, while a lots of geodesics on surface have complicated shapes. Goal of this research is to find on what surfaces are u- and v- parameter curves geodesics. Developable surfaces that contain a given plane curve as a geodesic are studied in the article, whereas the plane curve is also an initial u-parameter curve on that surface. Parametric equations of the minimal surfaces that contain an epicycloid as a geodesic are also given. Visualization of geodesics was done in  Mathematica.
Keywords: Geodesics; u- and v- parameter curve; Developable surface; Minimal surface