33 citations · 122 across the 17 of their papers we have counts for
20 papers
On singularities of the Gauss map components of surfaces in
W. Domitrz, L. I. Hernández-Martínez, F. Sánchez-Bringas
The Gauss map of a generic immersion of a smooth, oriented surface into is an immersion. But this map takes values on the Grassmanian of oriented 2-planes in $\mathbb…
Local invariants of divergence-free webs
Wojciech Domitrz, Marcin Zubilewicz
The objects of our study are webs in the geometry of volume-preserving diffeomorphisms. We introduce two local invariants of divergence-free webs: a differential one, directly rela…
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 Geometry of the Secant Caustic of a Planar Curve
W. Domitrz, M. C. Romero Fuster, M. Zwierzyński
The secant caustic of a planar curve is the image of the singular set of the secant map of . We analyse the geometrical properties of the secant caustic of a planar curve, i…
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…
On local invariants of singular symplectic forms
Wojciech Domitrz
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a -dimensional manifold. In the -analyt…
How can a clairvoyant particle escape the exclusion process?
Rangel Baldasso, Augusto Teixeira
We study a detection problem in the following setting: On the one-dimensional integer lattice, at time zero, place nodes on each site independently with probability an…
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…
Singularities of affine equidistants: extrinsic geometry of surfaces in 4-space
W. Domitrz, S. Janeczko, P. de M. Rios +1
For a generic embedding of a smooth closed surface into , the subset of which is the affine -equidistant of appears as the discriminant set of…
Even Dimensional Improper Affine Spheres
Marcos Craizer, Wojciech Domitrz, Pedro de M. Rios
There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while t…
The Wigner caustic on shell and singularities of odd functions
Wojciech Domitrz, Miriam Manoel, Pedro de M. Rios
We study the Wigner caustic on shell of a Lagrangian submanifold L of affine symplectic space. We present the physical motivation for studying singularities of the Wigner caustic o…
Zero-dimensional symplectic isolated complete intersection singularities
Wojciech Domitrz
We study the local symplectic algebra of the 0-dimensional isolated complete intersection singularities. We use the method of algebraic restrictions to classify these symplectic si…
Symplectic Sμ singularities
Wojciech Domitrz, Żaneta Trȩbska
We study the local symplectic algebra of the 1-dimensional isolated complete intersection singularity of type Sμ. We use the method of algebraic restrictions to classify symplectic…
Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds
Wojciech Domitrz, P. de M. Rios
We define the Global Centre Symmetry set (GCS) of a smooth closed m-dimensional submanifold M of R^n, , which is an affinely invariant generalization of the centre of a…
Symplectic , singularities and Lagrangian tangency orders
Wojciech Domitrz, Żaneta Trȩbska
We study the local symplectic algebra of curves. We use the method of algebraic restrictions to classify symplectic singularities. We define discrete symplectic invariants -…
Local symplectic algebra of quasi-homogeneous curves
Wojciech Domitrz
We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold. We use the method of algebraic restrictions to classify symplectic singularities of quasi-…
Reductions of locally conformal symplectic structures and de Rham cohomology tangent to a foliation
Wojciech Domitrz
We propose a produre of reduction a locally conformal symplectic structure. This procedure of reduction can be applied to wide class of submanifolds. There are no local obstruction…