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

TL;DR

This paper classifies the singular points of real surfaces in three-dimensional space that contain two circles through every point, providing insights into their topology and how circles interact with these singularities.

Contribution

It offers a complete classification of singular loci for surfaces with two circles through each point, advancing understanding of their geometric and topological properties.

Findings

Classification of singular loci in such surfaces

Description of circle interactions with singularities

Topological insights into the structure of these surfaces

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.