3 citations · 4 across the 6 of their papers we have counts for
6 papers
Curvature Functionals for Curves in the Equi-Affine Plane
Steven Verpoort
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constrain…
Some Modifications of the Theorem of Beltrami
Steven Verpoort
The two main topics of this text are as follows: Firstly, three modifications of the theorem of Beltrami will be presented for diffeomorphisms between Riemannian manifolds and a sp…
A Characterisation of Manhart's Relative Normal Vector Fields
Steven Verpoort
In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differen…
On the Inner Curvature of the Second Fundamental Form of a Surface in the Hyperbolic Space
Steven Verpoort
The object of study of this article is compact surfaces in the three-dimensional hyperbolic space with a positive-definite second fundamental form. It is shown that several conditi…
The Mean Curvature of the Second Fundamental Form of a hypersurface
Stefan Haesen, Steven Verpoort
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 curvatu…
On the Area Functional of the Second Fundamental Form of Ovaloids
Steven Verpoort
The expression for the variation of the area functional of the second fundamental form of a hypersurface in a Euclidean space involves the so-called "mean curvature of the second f…