Symmetry and uniqueness of parabolic affine spheres.
Symplectic applicability of Lagrangian surfaces.
The classification of 3-dimensional locally strongly convex homogeneous affine hypersurfaces.
The convex floating body.
The fundamental theorems of curves and hypersurfaces in centro-affine geometry.
The Killing Tensors on an -dimensional Manifold with -structure
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine -structure and discuss possible applications of obtained results in Riemannian geometry.
The Monge-Ampère equation and affine maximal surfaces.
The osculating hyperquadrics of the three-component distribution in affine space
Thomsen Surfaces in Affine 4-Space.
Torsion Free Connections, Topology, Geometry and Differential Operators on Smooth Manifolds
Traceless cubic forms on statistical manifolds and Tchebychev geometry
Geometry of traceless cubic forms is studied. It is shown that the traceless part of the cubic form on a statistical manifold determines a conformal-projective equivalence class of statistical manifolds. This conformal-projective equivalence on statistical manifolds is a natural generalization of conformal equivalence on Riemannian manifolds. As an application, Tchebychev type immersions in centroaffine immersions of codimension two are studied.
Translation foliations of codimension one on compact affine manifolds
Consider two foliations and , of dimension one and codimension one respectively, on a compact connected affine manifold . Suppose that ; and . In this paper we show that either is given by a fibration over , and then has a great degree of freedom, or the trace of is given by a few number of types of curves which are completely described. Moreover we prove that has a transverse affine structure.
Two-parametric systems of three-dimensional spaces in a unimodular six-dimensional affine space
Über die isotropoen Gegenstücke der Minimalfläche von Scherk.
Über geschlossene affine Zwangläufe in der Ebene.
Un survol de la théorie des variétés affines
Une correspondance par parallélisme partiel entre deux variétés réglées de l’espace
Variational problems and PDEs in affine differential geometry
This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss variational problems in equiaffine differential geometry, centroaffine differential geometry and relative differential geometry, which have been studied by Blaschke [Bla], Chern [Ch], C. P. Wang [W], Li-Li-Simon [LLS], and Calabi [Ca-II]. We first derive the Euler-Lagrange equations in these settings; these equations are complicated, strongly nonlinear fourth order PDEs. We...
Zur Affinoberfläche konvexer Körper.
Zur äquiformen Geometrie in der Ebene
Im Artikel werden die Integral- und Differentialgrundinvarianten (Bogen, Krümmung) der ebenen Kurve angesichts der äquiformen Gruppe (-Gruppe) bei der Anwendung der komplexen Symbolik hergeleitet. Weiter werden die -minimalen Kurven, -Geraden und -Kreise von der -Geometrie festgestellt; im euklidischen Modell handelt es sich um die Geraden, Kreise und logarithmischen Spiralen.