Curves with Prescribed Curvature and Associated Surfaces
DOI:
https://doi.org/10.17268/sel.mat.2025.02.12Keywords:
CPD surfaces, prescribed curvature, catenaries, principal directionAbstract
In this work, we study surfaces with a canonical principal direction (CPD surfaces) under the simultaneous prescription of two extrinsic geometric invariants: one principal curvature and the support function. Based on these prescriptions, we reformulate the first and second fundamental forms, which enables us to construct explicit examples of such surfaces. Finally, we show that when the curvature of the profile curve is constant, that is, when one of the principal curvatures is constant, the corresponding CPD surface is a tubular surface.
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