Metadata
Y. Liu, O. Pirahmad, H. Wang, D. L. Michels, and H. Pottmann.
Helical Surfaces with a Constant Ratio of Principal Curvatures.
Contributions to Algebra and Geometry, Springer (2022).
Helical Surfaces with a Constant Ratio of Principal Curvatures
Follow @csgKAUSTAbstract
We determine all helical surfaces in three-dimensional Euclidean space which possess a constant ratio a:=κ1/κ2 of principal curvatures (CRPC surfaces), thus providing the first explicit CRPC surfaces beyond the known rotational ones. Our approach is based on the involution of conjugate surface tangents and on well chosen generating profiles such that the characterizing differential equation is sufficiently simple to be solved explicitly. We analyze the resulting surfaces, their behavior at singularities that occur for a>0, and provide an overview of the possible shapes.
