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math.DG2009
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…
math.DG2009
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…
math.DG2009
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…