# Flat point

From Encyclopedia of Mathematics

A point on regular surface at which the osculating paraboloid degenerates to a plane. At a flat point the Dupin indicatrix is not defined, the Gaussian curvature is equal to zero and the second fundamental form and all remaining curvatures are also equal to zero.

A point at which the torsion of a curve vanishes is called a flat point of the spatial curve.

#### Comments

A flat point is sometimes called a planar point. The terminology of course derives from the curvature zero property.

#### References

[a1] | C.C. Hsiung, "A first course in differential geometry" , Wiley (1981) pp. Chapt. 3, Sect. 4 |

**How to Cite This Entry:**

Flat point. D.D. Sokolov (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Flat_point&oldid=14781

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098