Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 51, No. 1, pp. 155169 (2010) 

The mean curvature of the second fundamental form of a hypersurfaceStefan Haesen and Steven VerpoortSimon Stevin Institute for Geometry, Wilhelminaweg 1, nn 2042 Zandvoort, The Netherlands, email: stefan.haesen@geometryinstitute.or; K. U. Leuven, Departement Wiskunde, Afdeling Meetkunde, Celestijnenlaan 200B bus 2400, 3001 Heverlee, Belgium, email: steven.verpoort@gmail.comAbstract: An expression for the first variation of the area functional of the second fundamental form is given for a hypersurface in a semiRiemannian space. The concept of the ``mean curvature of the second fundamental form'' is then introduced for hypersurfaces in semiRiemannian spaces. Some characterisations of extrinsic hyperspheres in terms of this curvature are given. Keywords: second fundamental form, mean curvature, extrinsic hypersphere Classification (MSC2000): 53B25; 53A10, 53C42 Full text of the article:
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