47 citations · 313 across the 74 of their papers we have counts for
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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…
On three-periodic trajectories of multi-dimensional dual billiards
Serge Tabachnikov
We consider the dual billiard map with respect to a smooth strictly convex closed hypersurface in linear 2m-dimensional symplectic space and prove that it has at least 2m distinct…