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On the total mean curvature of a nonrigid surface. (Russian, English) Zbl 1224.53004
Sib. Mat. Zh. 50, No. 5, 963-966 (2009); translation in Sib. Math. J. 50, No. 5, 757-759 (2009).
Summary: Using Green’s theorem, we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field, which immediately yields the following well-known theorem: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.
MSC:
53A05 Surfaces in Euclidean and related spaces
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