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4 papers · 2 filters
Converse Sturm-Hurwitz-Kellogg theorem and related results
S. Tabachnikov
The classical Sturm-Hurwitz-Kellogg theorem asserts that a function, orthogonal to an n-dimensional Chebyshev system on a circle, has at least n+1 sign changes. We prove the conver…
Self-dual polygons and self-dual curves
Dmitry Fuchs, Serge Tabachnikov
We study projectively self-dual polygons and curves in the projective plane. Our results provide a partial answer to problem No 1994-17 in the book of Arnold's problems.
Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
Camille Laurent-Gengoux, Mathieu Stienon, Ping Xu
We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in t…
Geodesics on an ellipsoid in Minkowski space
D. Genin, B. Khesin, S. Tabachnikov
We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riema…