On the total mean curvature of non-rigid surfaces

Details On the total mean curvature of non-rigid surfaces On the total mean curvature of non-rigid surfaces

2008-11-29

arxiv.org/abs/0812.0053v1

Siberian Math. J. 50, no. 5 (2009), 757-759

Mathematics

Differential Geometry

4 pages

Scientific paper

10.1007/s11202-009-0087-3

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 and obtain the following well-known theorem as an immediate
consequence: the total mean curvature of a closed smooth surface in the
Euclidean 3-space is stationary under an infinitesimal flex.

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