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First variation of area formula : ウィキペディア英語版 | First variation of area formula In Riemannian geometry, the first variation of area formula relates the mean curvature of a hypersurface to the rate of change of its area as it evolves in the outward normal direction. Let be a smooth family of oriented hypersurfaces in a Riemannian manifold ''M'' such that the velocity of each point is given by the outward unit normal at that point. The first variation of area formula is : where ''dA'' is the area form on induced by the metric of ''M'', and ''H'' is the mean curvature of . The normal vector is parallel to where is the tangent vector. The mean curvature is parallel to the normal vector. ==References==
*Chow, Lu, and Ni, "Hamilton's Ricci Flow." AMS Science Press, GSM volume 77, 2006.
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