Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 155-169 (2010)
The mean curvature of the second fundamental form of a hypersurface
Stefan Haesen and Steven VerpoortSimon Stevin Institute for Geometry, Wilhelminaweg 1, nn 2042 Zandvoort, The Netherlands, e-mail: firstname.lastname@example.org; K. U. Leuven, Departement Wiskunde, Afdeling Meetkunde, Celestijnenlaan 200B bus 2400, 3001 Heverlee, Belgium, e-mail: email@example.com
Abstract: An expression for the first variation of the area functional of the second fundamental form is given for a hypersurface in a semi-Riemannian space. The concept of the ``mean curvature of the second fundamental form'' is then introduced for hypersurfaces in semi-Riemannian 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
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Electronic version published on: 27 Jan 2010. This page was last modified: 28 Jan 2013.