Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 155-169 (2010)

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The mean curvature of the second fundamental form of a hypersurface

Stefan Haesen and Steven Verpoort

Simon Stevin Institute for Geometry, Wilhelminaweg 1, nn 2042 Zandvoort, The Netherlands, e-mail: stefan.haesen@geometryinstitute.or; K. U. Leuven, Departement Wiskunde, Afdeling Meetkunde, Celestijnenlaan 200B bus 2400, 3001 Heverlee, Belgium, e-mail:

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.

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