# Parabolic point

From Diffgeom

Template:Point property on regular surface

## Contents

## Definition

A point on a regular surface is termed a **parabolic point** if it satisfies the following equivalent conditions:

- The shape operator at the point is a nonzero, but singular, matrix
- Exactly one of the principal curvatures is zero
- The Gaussian curvature is zero but the mean curvature is not