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.
Differential Geometry of Real Monge-Ampère Foliations.
Differential geometry of surfaces
Dual Connections and Affine Geometry.
Eigenvalues of a natural operator of centro-affine and graph hypersurfaces.
Eine äquiaffine Charakterisierung der Cardan-Bewegung mittels der höheren Wendepole.
Equipping distributions for linear distribution
In this paper there are discussed the three-component distributions of affine space . Functions , which are introduced in the neighborhood of the second order, determine the normal of the first kind of -distribution in every center of -distribution. There are discussed too normals and quasi-tensor of the second order . In the same way bunches of the projective normals of the first kind of the -distributions were determined in the differential neighborhood of the second and third order.
General Affine Differential Geometry for Low Codimension Immersions.
General-affine invariants of plane curves and space curves
We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups and , respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective...
Geometric methods for solving Codazzi and Monge-Ampère equations.
Géométrie différentielle affine des hypersurfaces