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The expression for the variation of the area functional of the secondfundamental form of a hypersurface in a Euclidean space involves the so-called"mean curvature of the second fundamental form". Several new characteristicproperties of (hyper)spheres, in which the mean curvature of the secondfundamental form occurs, are given. In particular, it is shown that the spheresare the only ovaloids which are a critical point of the area functional of thesecond fundamental form under various constraints.

ON THE AREA FUNCTIONAL OF THE SECOND FUNDAMENTAL FORM OF OVALOIDS