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Difference between revisions of "Base of a deformation"

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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.
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A [[Conjugate net|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.
  
 
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====References====

Latest revision as of 14:16, 1 May 2014

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=17621
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article