Relations entre les rayons de courbure de quelques systèmes de courbes
Relaxed hyperelastic curves
We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space E³, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases.
Remark on bilinear operations on tensor fields
This short note completes the results of [3] by removing the locality assumption on the operators. After providing a quick survey on (infinitesimally) natural operations, we show that all the bilinear operators classified in [3] can be characterized in a completely algebraic way, even without any continuity assumption on the operations.
Remark on one theorem of R. Schneider
Remark on surfaces in satisfying certain relations between covariant derivatives of the mean and Gauss curvatures
Remarks on algebraic concomitants of the Riemann-Christoffel curvature tensor in a three-dimensional space
Remarks on differential concomitants of densities
Remarks on Grassmannian Symmetric Spaces
The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for -graded parabolic geometries and for almost Grassmannian structures, in particular. As an application of two general constructions with parabolic geometries, we present an example of non-flat Grassmannian symmetric space. Next we observe there is a distinguished torsion-free...
Remarks on the Darboux transform of isothermic surfaces.
Remarks on the Isoperimetric Inequality for Multiply-connected H-Surfaces.
Remarks on the Stability of Minimal Submanifolds of IRn.
Remarks on the symmetries of planar fronts.
A front is the projection on the plane of a Legendrian immersion of a circle in the space of the contact elements of that plane. I analyze the symmetries of a generic front with respect to the group generated by the involutions reversing the orientation of the plane, the orientation of the preimage circle and the coorientation of the contact plane.
Remarque sur la note de M. Floquet relative à l'intégration de l'équation d'Euler
Remarque sur une equation differentielle du premier ordre
Remarques sur les variétés conformément plates.
Remarques sur une classe générale de surfaces, et en particulier sur la surface lieu des points dont la somme des distances à deux droites fixes est constante
Reper sítě na ploše
Reper sítě na ploše v trojrozměrném afinním prostoru
Reperáž systému anholonomních subvariet trojrozměrné variety v pětirozměrném ekviafinním prostoru
Representation of curves of constant width in the hyperbolic plane.