View source for Base of a deformation

A [[Conjugate net|conjugate net]] on a surface <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015320/b0153201.png" /> and its deformation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015320/b0153202.png" /> outside their points of congruence. The base of a deformation is characterized by the fact that the bend — the relation between the normal curvatures <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015320/b0153203.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015320/b0153204.png" /> at isometrically-corresponding points of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015320/b0153205.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015320/b0153206.png" /> along corresponding directions — has extremal values along the directions of the base of the deformation.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  V.F. Kagan,   "Foundations of the theory of surfaces in a tensor setting" , '''2''' , Moscow-Leningrad  (1948)  (In Russian)</TD></TR></table>



====Comments====
For more references on the topic of deforming or bending surfaces, cf. the article [[Deformation, isometric|Deformation, isometric]].