Geradenfamilien, Enveloppen und Evoluten.
Gheorge Titeica and affine differential geometry.
Higher order Codazzi tensors on conformally flat spaces.
Homogeneous affine hypersurfaces with rank one shape operators.
Homogeneous parabolic surfaces in .
Homogeneous surfaces in the equiaffine space R⁴
Hypersurfaces with almost complex structures in the real affine space
We study affine hypersurface immersions , where M is an almost complex n-dimensional manifold. The main purpose is to give a condition for (M,J) to be a special Kähler manifold with respect to the Levi-Civita connection of an affine fundamental form.
Hypersurfaces with constant inner curvature of the second fundamental form, and the non-rigidity of the sphere.
Hypersurfaces with parallel affine curvature tensor R*
In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space . In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.
Improper affine spheres and δ-invariants
We introduce an inequality for graph hypersurfaces and prove a decomposition theorem in case equality holds.
Indefinite affine hyperspheres admitting a pointwise symmetry. I.
Indefinite affine hyperspheres admitting a pointwise symmetry. II.
Inequalities for radial Blaschke-Minkowski homomorphisms
We establish Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms, which in special cases yield some new results for intersection bodies. Moreover, we obtain two monotonicity inequalities for radial Blaschke-Minkowski homomorphisms.
Infinitesimal rigidity of surfaces in
Inner parallel curves and domains in the equiaffine geometry.
Invariance groups of relative normals
We investigate a two-parameter family of relative normals that contains Manhart's one-parameter family and the centroaffine normal. The invariance group of each of these normals is classified, and variational problems are studied. The results are Euler-Lagrange equations for the hypersurfaces that are critical with respect to the area functionals of the induced and semi-Riemannian volume forms and a classification of the critical hyperovaloids in the two-parameter family.
Minkowski minimal surfaces in with minimal focal surfaces.
Minkowski valuations intertwining the special linear group
All continuous Minkowski valuations which are compatible with the special linear group are completely classified. One consequence of these classifications is a new characterization of the projection body operator.
Neue Erzeugungen der Minmalflächen von G. Thomsen.
Noncomplete affine structures on Lie algebras of maximal class.