an:05947261
Zbl 1222.53006
Alexandrov, Victor
New manifestations of the Darboux's rotation and translation fields of a surface
EN
N. Z. J. Math. 40, 59-65 (2010).
00286183
2010
j
53A05 53A04
infinitesimal bending; simply connected surface; total mean curvature
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).