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New manifestations of the Darboux’s rotation and translation fields of a surface. (English) Zbl 1222.53006
Summary: We show how the rotation and translation fields of a surface, introduced by Gaston Darboux, may be used to obtain short proofs of a well-known theorem (asserting that the total mean curvature of a surface is stationary under an infinitesimal bending) and a new theorem (asserting that every infinitesimal bending of any simply connected closed surface \(S\subset\mathbb R^3\) is orthogonal to \(S\) at least at two points).

MSC:
53A05 Surfaces in Euclidean and related spaces
53A04 Curves in Euclidean and related spaces
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