# Peterson surface

From Encyclopedia of Mathematics

A surface carrying a conjugate net of conical or cylindrical lines forming a principal base for a deformation (see Deformation over a principal base). For example, a canal surface, a surface of translation (cf. Transport surface) and a rotational surface (cf. Rotation surface) are Peterson surfaces. The rotation indicatrix of a Peterson surface is a straight conoid (in particular, it is a helicoid for a canal surface, and a hyperbolic paraboloid for a surface of translation). These surfaces were first considered by K.M. Peterson as examples of surfaces allowing of a deformation over a principal base.

#### Comments

For references see also Peterson correspondence.

**How to Cite This Entry:**

Peterson surface. I.Kh. Sabitov (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Peterson_surface&oldid=15404

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098