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

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

2009-10-27

arxiv.org/abs/0910.5164v1

New Zealand Journal of Mathematics, 40 (2010), 59-65

Mathematics

Differential Geometry

6 pages

Scientific paper

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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