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Jul 26, 2023 at 13:27 comment added Math_Newbie @ABIM Because the injectivity radius on $<\operatorname{SO}(n),g)$ is at-least $\pi/\sqrt{2}$?
Jul 26, 2023 at 13:26 vote accept Math_Newbie
Jul 21, 2023 at 13:02 comment added ABIM Let me also add that "small enough" means in a ball of radius $R$ where $\pi/\sqrt{2} \le R\le \pi \sqrt{2 \lfloor n/2\rfloor} $; where $R$ is the injectivity radius on $(SO(n),g)$ and $g$ is the aforementioned bi-invariant metric.
Jul 21, 2023 at 4:07 history answered Ramiro Lafuente CC BY-SA 4.0