Geometric analysis demonstrates geodesic parameter curve behavior across developable and minimal surfaces, highlighting analytical constructions for complex path geometries.
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.
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Maksimović et al. (2020) studied this question.
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