2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228457An 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. Some characterisations of extrinsic hyperspheres in terms of this curvature are given.25 pages; 2 figures. As compared to previous versions only minor corrections have been made. A shorter version of this article is accepted for publication in Beiträge zur Algebra und GeometrieDifferential Geometry53A10, 53B25, 53C42text