Calabi Conjecture on Hyperbolic Affine Hyperspheres.
Calabi conjecture on hyperbolic affine hyperspheres (2).
Canonical equiaffine hypersurfaces in R n + 1.
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,...
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
Classification of five dimensional hypersurfaces with affine normal parallel cubic form.
Classification of homogeneous submanifolds in homogeneous spaces.
Classification of surfaces in which are centroaffine-minimal and equiaffine-minimal.
Codazzi structures induced by minimal affine immersions
We give a necessary and sufficient condition for a Codazzi structure to be realized as a minimal affine hypersurface or a minimal centroaffine immersion of codimension two.
Complex affine transversal bundles for surfaces in .
Complex surfaces in ℂ⁴ with recurrent shape operators
We study complex affine surfaces in ℂ⁴ with the transversal bundle defined by Nomizu and Vrancken. We classify the surfaces that have recurrent shape operators and parallel transversal metric.
Conjugate Connections and Radon's Theorem in Affine Differential Geometry.
Contributions to Affine Surface Area.
Cubic form geometry for surfaces in .
Curvature functionals for curves in the equi-affine plane
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.