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

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.

Improved exposition, 4 figures added

Cited by in corpus (6)

• Improved bounds for incidences between points and circles
• Surfaces containing two circles through each point
• Surfaces containing two circles through each point and Pythagorean 6-tuples
• Surfaces that are covered by two pencils of circles
• Surfaces containing two isotropic circles through each point
• Shapes of surfaces that contain a great and a small circle through each point