15 citations · 33 across the 7 of their papers we have counts for
10 papers
Existence and non-existence of skew branes
S. Tabachnikov, Yu. Tyurina
Following recent work by Ghomi, Solomon and Tabachnikov, we study geometry and topology of skew branes. A skew brane is a codimension 2 submanifold in affine space such that the ta…
Non-existence of n-dimensional T-embedded discs in R^2n
G. Stojanovic, S. Tabachnikov
A manifold is T-embedded into an affine space if its tangent spaces at distinct points are disjoint. We prove that an n-dimensional disc cannot be T-embedded into 2n-dimensional sp…
Tire track geometry: variations on a theme
Serge Tabachnikov
We study closed smooth convex plane curves enjoying the following property: a pair of points can traverse so that the distances between and along the curve an…
Totally skew embeddings of manifolds
M. Ghomi, S. Tabachnikov
We obtain bounds on the least dimension of an affine space that can contain an -dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct p…
Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem
Serge Tabachnikov
We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law "angle of incidence eq…
On skew loops, skew branes and quadratic hypersurfaces
Serge Tabachnikov
A skew brane is an immersed codimension 2 submanifold in affine space, free from pairs of parallel tangent spaces. Using Morse theory, we prove that a skew brane cannot lie on a qu…