For hypersurfaces, one classically computes the evolution (in the normal direction) of the area form as mean curvature, and the evolution of the mean curvature as the stability operator. I'm lucky enough to be in a case where I have a foliation of totally geodesic hypersurfaces. As such, I would like to compute something like the evolution of $|A|^2$ with $A$ being the second fundamental form of the hypersurface. I'm sure this is well-known, but I'm having trouble pinning down a reference to check my calculations. Does anyone know of any?
2026-03-25 06:31:53.1774420313
Evolution of second fundamental form
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