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arXiv · 0910.5164

New manifestations of the Darboux's rotation and translation fields of a surface

Victor Alexandrov
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Abstract

We show how the rotation and translation fields of a surface, introduced by G. Darboux, may be used to obtain short proofs of a well-known theorem (that reads that the total mean curvature of a surface is stationary under an infinitesimal bending) and a new theorem (that reads that every infinitesimal flex of any simply connected closed surface is orthogonal to the surface at least at two points).

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Victor Alexandrov. 2009-10-27. New manifestations of the Darboux's rotation and translation fields of a surface. https://arxiv.org/abs/0910.5164

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