6 papers
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…
Order of tangency between manifolds
Wojciech Domitrz, Piotr Mormul, Piotr Pragacz
We study the order of tangency between two manifolds of same dimension and give that notion three quite different geometric interpretations. Related aspects of the order of tangenc…
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…
Symplectic singularity of curves with semigroups (4,5,6,7), (4,5,6) and (4,5,7)
Fausto Assunção de Brito Lira, Wojciech Domitrz, Roberta Wik Atique
We study the local symplectic algebra of curves with semigroups , and . We use the method of algebraic restrictions to parameterized curves as in \cit…