Generatrix of catenoid of space 3-form

Анотація

Constant mean curvature surfaces of revolution in euclidean 3-space are known as surfaces of Ch. Delaunay. They possess one remarkable property: their profile curves (generatrices) are the trajectories of focuses of conic sections by its rolling along the straight line. Analogous construction is realized in the space forms H ³ and S ³ in the case of minimal surfaces of revolution and the following theorem is proved.

Theorem. Generatrix of catenoid of revolution of space form H ³(S³) is the trajectory of focus of hyperbolic (spherical) parabola by its rolling along the geodesic ray.