Timeline for Geodesic sphere in the octonion projective plane
Current License: CC BY-SA 4.0
3 events
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| Apr 30, 2020 at 0:56 | comment | added | Renato G. Bettiol | @DonghwiSeo: This follows from analyzing the isotropy representation of the action. Namely, the subgroup of Spin(9) that fixes a given point on S^15 is isomorphic to Spin(7), and its isotropy representation splits as a direct sum of 2 irreducible modules, of dimensions 8 and 7. With a little work, you can see that these are respectively the horizontal and vertical space of the Hopf fibration. Sorry for the very late reply, NYC has been hard to live in lately.. | |
| Feb 4, 2020 at 11:30 | comment | added | Donghwi Seo | Thank you for confirming my question. How can we know that $Spin(9)$-homogeneous metrics on $S^{15}$ are canonical deformations of the round metric on $S^{15}$ with respect to the Hopf fibration? | |
| Dec 12, 2019 at 15:27 | history | answered | Renato G. Bettiol | CC BY-SA 4.0 |