Last geometric statement of Jacobi

In differential geometry and algebraic geometry, the last geometric statement of Jacobi is a conjecture named after Carl Gustav Jacob Jacobi. According to this conjecture, every caustic from any point ${\displaystyle p}$ on an ellipsoid other than umbilical points has exactly four cusps.

References

• Arnold, V. I. (1999), "Topological problems in wave propagation theory and topological economy principle in algebraic geometry", The Arnoldfest (Toronto, ON, 1997), Fields Inst. Commun., 24, Providence, RI: Amer. Math. Soc., pp. 39–54, MR 1733567. See in particular p. 45.
• Sinclair, R. (2003), "On the last geometric statement of Jacobi", Experimental Mathematics, 12 (4): 477–485, doi:10.1080/10586458.2003.10504515, MR 2043997.
• Sinclair, Robert; Tanaka, Minoru (2006), "Jacobi's last geometric statement extends to a wider class of Liouville surfaces", Mathematics of Computation, 75 (256): 1779–1808, doi:10.1090/S0025-5718-06-01924-7, MR 2240635.