Base of a deformation

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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.


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


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