Peterson surface

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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.


For references see also Peterson correspondence.

How to Cite This Entry:
Peterson surface. I.Kh. Sabitov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098