Ellipsoidal billiards in pseudo-Euclidean spaces and relativistic quadrics
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Publication:456745
DOI10.1016/j.aim.2012.06.004zbMath1252.37049arXiv1108.4552OpenAlexW1980309091MaRDI QIDQ456745
Milena Radnović, Vladimir Dragović
Publication date: 16 October 2012
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1108.4552
Minkowski spaceconfocal quadricslight-like billiard trajectoriesperiodic billiard trajectoriesPoncelet theoremtropic curves
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Cites Work
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- A survey of the analytical description of periodic elliptical billiard trajectories
- Hyperelliptic Jacobians as billiard algebra of pencils of quadrics: Beyond Poncelet porisms
- Geometry of integrable billiards and pencils of quadrics
- Pseudo-Riemannian geodesics and billiards
- On Cayley's explicit solution to Poncelet's porism
- Singularities of \(\mathbb{R} P^2\)-valued Gauss maps of surfaces in Minkowski 3-space
- Algebraic curves and integrable systems: Geodesics of quadrics
- Geodesics on an ellipsoid in Minkowski space
- Mathematical general relativity: A sampler
- Confocal Conics in Space-Time
- LIGHTLIKE DEVELOPABLES IN MINKOWSKI 3-SPACE
- Elliptical billiard systems and the full Poncelet’s theorem in n dimensions
- On periodical trajectories of the billiard systems within an ellipsoid in Rd and generalized Cayley’s condition
