-гладкие изометрические погружения
-гладкие поверхности ограниченной внешней положительной кривизны
Calcul du rayon de la sphère inscrite dans le tétraèdre
Characterizations of the sphere by the curvature of the second fundamental form
Characterizations of the sphere in by means of the pseudoparallel mean curvature vector field
Circular cone and its Gauss map
The family of cones is one of typical models of non-cylindrical ruled surfaces. Among them, the circular cones are unique in the sense that their Gauss map satisfies a partial differential equation similar, though not identical, to one characterizing the so-called 1-type submanifolds. Specifically, for the Gauss map G of a circular cone, one has ΔG = f(G+C), where Δ is the Laplacian operator, f is a non-zero function and C is a constant vector. We prove that circular cones are characterized by being...
Classification der Flächen nach der Transformationsgruppe ihrer geodätischen Curven [Book]
Closed surfaces with different shapes that are indistinguishable by the SRNF
The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [5], provides a way of representing immersed surfaces in , and equipping the set of these immersions with a “distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of . Thus, it induces a distance function on the shape space of immersions, i.e., the space...
Complete classification of surfaces with a canonical principal direction in the Euclidean space 3
In the present paper we classify all surfaces in 3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space 3 is the catenoid.
Contribution to the characterization of the sphere in
Convexity of Capillary Surfaces in the Outer Space.
Courbure discrète ponctuelle
Soient une surface de l’espace euclidien et un ensemble de triangles euclidiens formant une approximation linéaire par morceaux de autour d’un point la courbure discrète ponctuelle au sommet de est, par définition, le quotient du défaut angulaire par la somme des aires des triangles ayant comme sommet. Un problème naturel est d’estimer la différence entre cette courbure discrète et la courbure lisse de en Nous présentons dans cet article des résultats obtenus dans [4], [5],...
Courbure en un point d'une surface définie par son équation tangentielle.
Courbure en un point multiple d'une surface.
Cubic ruled surfaces with constant distribution parameter in .
Curvature and -strict convexity.
Curvature computations on surfaces in -space
Curvatures of conflict surfaces in Euclidean 3-space
This article extends to three dimensions results on the curvature of the conflict curve for pairs of convex sets of the plane, established by Siersma [3]. In the present case a conflict surface arises, equidistant from the given convex sets. The Gaussian, mean curvatures and the location of umbilic points on the conflict surface are determined here. Initial results on the Darbouxian type of umbilic points on conflict surfaces are also established. The results are expressed in terms of the principal...
Curve shortening makes convex curves circular.
Curves of constant breadth