Timeline for Comparison of sum of vectors and exponential map on a Riemannian manifold
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2021 at 22:01 | comment | added | Sebastian Goette | In a space of constant curvature, there are trigonometric formulas that you can apply (for the first two vectors). Then you have to "guess" the next angle and continue ... | |
| Nov 18, 2021 at 19:55 | comment | added | M.R.Karimi | Very good idea indeed! However, I was thinking that with Topogonov, I might be able to transfer the problem to a space with constant sectional curvature $\delta$. It is still unclear for me how to deal with this problem even in that case... (scratching my head) | |
| Nov 18, 2021 at 12:25 | comment | added | Sebastian Goette | Only a vague idea: have you tried the Toponogov comparison theorem? This and many others are covered in a book by Cheeger and Ebin. Maybe you find something helpful there. Of course, that theorem would at first help only with two vectors, because you would need a good estimate on $\exp^{-1}_{p_0}(p_2)$ to continue. But my impression is that global comparison results might be more helpful than Jacobi field comparison. | |
| Nov 17, 2021 at 11:07 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Nov 17, 2021 at 10:30 | history | asked | M.R.Karimi | CC BY-SA 4.0 |