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Bonnet theorem

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This article is about the Bonnet theorem in differential geometry. For Bonnet's theorem in classical mechanics, see Bonnet's theorem.

In the mathematical field of differential geometry, more precisely, the theory of surfaces in Euclidean space, the Bonnet theorem states that the first and second fundamental forms determine a surface in R3 uniquely up to a rigid motion.[1] It was proven by Pierre Ossian Bonnet in about 1860.

This is not to be confused with the Bonnet–Myers theorem or Gauss–Bonnet theorem.

References

  1. ^ Toponogov, Victor Andreevich (2006), Differential geometry of curves and surfaces, Boston, MA: Birkhäuser Boston, Inc., p. 132, ISBN 978-0-8176-4384-3, MR 2208981.
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