Timeline for Conjugate points and Jacobi matrices
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 21, 2020 at 11:12 | comment | added | Ali | Many thanks Chee. | |
| May 20, 2020 at 17:36 | comment | added | Chee | hi Ali, just a comment: (a) look at the 2nd part of the proof of Proportion 2.5.8 and the 2nd paragraph of the proof of Theorem 2.1.12 in 2nd edition of Klingenberg's book "Riemannian geometry". These give sufficient conditions (for conjugate points) on the determinant of the matrix formed by Jacobi fields normal to a geodesic; (b) look at the proof of Lemma 5.4 of Sakai's "Riemannian geometry". This shows how to use the tangent map of the exponential map to construct such Jacobi fields (a classic technique) and how the determinant comes into play; (c) modify the skills in (b) if needed | |
| Feb 16, 2020 at 11:02 | history | asked | Ali | CC BY-SA 4.0 |