A surface containing a line and a circle through each point is a quadric

TL;DR

This paper proves that any surface in three-dimensional space containing a line and a circle through every point must be a quadric surface, and explores classifications of such surfaces with multiple circles.

Contribution

It establishes that surfaces with a line and a circle through each point are necessarily quadrics, providing a classification framework for surfaces with multiple circles.

Findings

Surfaces with a line and a circle through each point are quadrics.

Classification results for surfaces with multiple circles.

Characterization of such surfaces in real 3-space.

Abstract

We prove that a surface in real 3-space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point.