4 papers · 1 filter
Unimodular families of symmetric matrices
Wojciech Domitrz, Shyuichi Izumiya, Hiroshi Teramoto
We introduce the volume-preserving equivalence among symmetric matrix-valued map-germs which is the unimodular version of Bruce's -equivalence. The key concept to dedu…
Singular Improper Affine Spheres from a given Lagrangian Submanifold
Marcos Craizer, Wojciech Domitrz, Pedro de M Rios
Given a Lagrangian submanifold of the affine symplectic -space, one can canonically and uniquely define a center-chord and a special improper affine sphere of dimension $2n…
Singular points of the Wigner caustic and affine equidistants of planar curves
W. Domitrz, M. Zwierzyński
In this paper we study singular points of the Wigner caustic and affine --equidistants of planar curves based on shapes of these curves. We generalize the Blaschke-Süss theorem…
The Gauss-Bonnet Theorem for coherent tangent bundles over surfaces with boundary and its applications
Wojciech Domitrz, Michał Zwierzyński
In [31,32,33] the Gauss-Bonnet formulas for coherent tangent bundles over compact oriented surfaces (without boundary) were proved. We establish the Gauss-Bonnet theorem for cohere…