Canonical equiaffine hypersurfaces in R n + 1.
Canonical form on a groupoid related to regular prolongations of Lie groups
Caractérisation des tissus de C2 dont le rang est maximal et qui sont linéarisables
Cauchy problems for discrete affine minimal surfaces
In this paper we discuss planar quadrilateral (PQ) nets as discrete models for convex affine surfaces. As a main result, we prove a necessary and sufficient condition for a PQ net to admit a Lelieuvre co-normal vector field. Particular attention is given to the class of surfaces with discrete harmonic co-normals, which we call discrete affine minimal surfaces, and the subclass of surfaces with co-planar discrete harmonic co-normals, which we call discrete improper affine spheres. Within this classes,...
Caustic of the three-dimensional ellipsoid. (Caustique de la surface ellipsoïdale à trois dimensions.)
Centroaffine differential geometry and its relations to horizontal submanifolds
We relate centroaffine immersions to horizontal immersions g of Mⁿ into or . We also show that f is an equiaffine sphere, i.e. the centroaffine normal is a constant multiple of the Blaschke normal, if and only if g is minimal.
Centroaffine surfaces with parallel traceless cubic form.
Centroaffinely homogeneous surfaces in .
Certain curvature characterizations of affine hypersurfaces
Ch flat curves in Euclidean space
Characterization of compact subsets of curves with ω-continuous derivatives
We give a characterization of compact subsets of finite unions of disjoint finite-length curves in ℝⁿ with ω-continuous derivative and without self-intersections. Intuitively, our condition can be formulated as follows: there exists a finite set of regular curves covering a compact set K iff every triple of points of K behaves like a triple of points of a regular curve. This work was inspired by theorems by Jones, Okikiolu, Schul and others that characterize compact subsets of...
Characterizations of conformally flat hypersurfaces
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
Chords and arclength of a closed space curve
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...
Circuminscribed polygons in a plane annulus
Each oval and a natural number n ≥ 3 generate an annulus which possesses the Poncelet's porism property. A necessary and sufficient condition of existence of circuminscribed n-gons in an annulus is given.
Classical differential geometry with Christoffel symbols of Ehresmann -connections
We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christoffel symbols of a symmetric Ehresmann -connection.
Classification der Flächen nach der Transformationsgruppe ihrer geodätischen Curven [Book]
Classification des densités vectorielles factorisées