On the Last Geometric Statement of Jacobi

DOI10.1080/10586458.2003.10504515zbMath1073.53007OpenAlexW2037899862WikidataQ56422996 ScholiaQ56422996MaRDI QIDQ4651439

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Publication date: 21 February 2005

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1087568023

zbMATH Keywords

cut locustriaxial ellipsoidcausticcuspsconjugate locus

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Software, source code, etc. for problems pertaining to differential geometry (53-04)

Related Items (9)

Bifurcations of the conjugate locus ⋮ The structure of the conjugate locus of a general point on ellipsoids and certain Liouville manifolds ⋮ The conjugate locus on convex surfaces ⋮ On Cusps of Caustics by Reflection: Billiard Variations on the Four Vertex Theorem and on Jacobi’s Last Geometric Statement ⋮ The conjugate locus in convex 3-manifolds ⋮ Cut loci and conjugate loci on Liouville surfaces ⋮ Jacobi’s last geometric statement extends to a wider class of Liouville surfaces ⋮ A Bound on the Number of Endpoints of the Cut Locus ⋮ Open problems on billiards and geometric optics

Uses Software

• Loki
• Thaw

Cites Work

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• Geodesics on the ellipsoid
• Distance function and cut loci on a complete Riemannian manifold
• An Eulerian method for capturing caustics
• High-frequency wave propagation by the segment projection method
• The theory of caustics and wave front singularities with physical applications
• Ray paths and caustics on a slightly oblate ellipsoid
• Fast-phase space computation of multiple arrivals
• Oscillatory integrals, lagrange immersions and unfolding of singularities
• Loki: Software for Computing Cut Loci

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