# Base of a deformation

From Encyclopedia of Mathematics

A conjugate net on a surface $F$ and its deformation $F^*$ outside their points of congruence. The base of a deformation is characterized by the fact that the bend — the relation between the normal curvatures $k$ and $k^*$ at isometrically-corresponding points of $F$ and $F^*$ along corresponding directions — has extremal values along the directions of the base of the deformation.

#### References

[1] | V.F. Kagan, "Foundations of the theory of surfaces in a tensor setting" , 2 , Moscow-Leningrad (1948) (In Russian) |

#### Comments

For more references on the topic of deforming or bending surfaces, cf. the article Deformation, isometric.

**How to Cite This Entry:**

Base of a deformation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Base_of_a_deformation&oldid=32025

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article