Self-intersections of surfaces that contain two circles through each point

Abstract

We classify the singular loci of real surfaces in three-space that contain two circles through each point. We characterize how a circle in such a surface meets this loci as it moves in its pencil and as such provide insight into the topology of the surface.

References in corpus (8)

• Darboux cyclides and webs from circles
• Curvature line parametrized surfaces and orthogonal coordinate systems. Discretization with Dupin cyclides
• Surfaces containing two circles through each point
• Surfaces containing two circles through each point and Pythagorean 6-tuples
• Kinematic generation of Darboux cyclides
• Translational and great Darboux cyclides
• Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces
• Using Algebraic Geometry to Reconstruct a Darboux Cyclide from a Calibrated Camera Picture