2 citations · 2 across the 6 of their papers we have counts for
5 papers · 1 filter
Dynamics and the Godbillon-Vey Class of C^1 Foliations
Steven Hurder, Rémi Langevin
Let F be a codimension-one, C^2-foliation on a manifold M without boundary. In this work we show that if the Godbillon--Vey class GV(F) \in H^3(M) is non-zero, then F has a hyperbo…
The geometry of canal surfaces and the length of curves in de Sitter space
Rémi Langevin, Gil Solanes
We find the minimal value of the length in de Sitter space of closed space-like curves with non-vanishing non-space-like geodesic curvature vector. These curves are in corresponden…
Space of subspheres and conformal invariants of curves
R. Langevin, J. O'Hara, S. Sakata
A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to Möbius transformations. We use the spaces of osculating circles and spheres t…
Dynamical behavior of Darboux curves
Ronaldo Garcia, Remi Langevin, Pawel Walczak
In 1872 G. Darboux defined a family of curves on surfaces of R^3 which are preserved by the action of the Mobius group and share many properties with geodesics. Here we characteriz…
Conformal arc-length as dimensional length of the set of osculating circles
Rémi Langevin, Jun O'Hara
The set of osculating circles of a given curve in $\SS^3$ forms a curve in the set of oriented circles in $\SS^3$. We show that its "-dimensional measure" with respect t…