Sur un élément du triangle rectiligne ; symédiane
Sur un théorème relatif à la théorie des enveloppes
Tangential Symmetries of Planar Curves and Space Curves
Tensor product surfaces of a Euclidean space curve and a Euclidean plane curve.
The centre symmetry set
A centrally symmetric plane curve has a point called it’s centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in . We investigate some of it’s properties, and begin the study of non-convex cases.
The characterization of the spherical timelike curves in 3-dimensional Lorentzian space.
The geodesic curvature and geodesic torsion of the intersection curve of two surfaces.
The isoperimetric inequality and the total absolute curvature of closed curves in spheres.
The Nash-Kuiper process for curves
A strictly short embedding is an embedding of a Riemannian manifold into an Euclidean space that strictly shortens distances. From such an embedding, the Nash-Kuiper process builds a sequence of maps converging toward an isometric embedding. In that paper, we describe this Nash-Kuiper process in the case of curves. We state an explicit formula for the limit normal map and perform its Fourier series expansion. We then adress the question of Holder regularity of the limit map.
The pedal point generation of circular curves of order three in the isotropic plane. (Die Fußpunkterzeugung der zirkulären Kurven 3. Ordnung in der isotropen Ebene.)
The rectifying developable and the spherical Darboux image of a space curve
In this paper we study singularities of certain surfaces and curves associated with the family of rectifying planes along space curves. We establish the relationships between singularities of these subjects and geometric invariants of curves which are deeply related to the order of contact with helices.
The role of symmetry and separation in surface evolution and curve shortening.
The rosettes.
The shape of a figure-eight under the curve shortening flow.
The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics
Théorie des courbes gauches
Timelike quaternion frame of a non-lightlike curve.
Total absolute curvature of curves in Lorentz Manifolds
Total curvature of non-differentiable curves.
Transnormale Isotopien und transnormale Kurven.