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The Congruence Theorem for Ovaloids

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1000)

Abstract

Let S and S* be two isometric surfaces (see I, 2.6). Let h be the isometry between S and S* and let u, v be parameters such that X(u,v) and X*(u,v) are corresponding points under the map h . Then S and S* have the same first fundamental forms; i.e.

$$ \left( {{\text{E,F,G}}} \right) = \left( {{\text{E*,F*,G*}}} \right) $$
(1)

.

Keywords

  • Quadratic Form
  • Line Element
  • Fundamental Form
  • Closed Surface
  • Common Zero

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© 1983 Springer-Verlag Berlin Heidelberg

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Hopf, H. (1983). The Congruence Theorem for Ovaloids. In: Differential Geometry in the Large. Lecture Notes in Mathematics, vol 1000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21563-0_13

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  • DOI: https://doi.org/10.1007/978-3-662-21563-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12004-9

  • Online ISBN: 978-3-662-21563-0

  • eBook Packages: Springer Book Archive