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May 31, 2018 at 19:06 comment added mme This would only apply in the octonion case if $\Bbb{OP}^2$ can be described as in the first sentence (the one-point compactification of the tautological line bundle over $\Bbb{OP}^1$). I don't know enough about octonions to know if this is the case. This (and of course Mikhail Katz' answer) verify the claim that the sphere bundle is the unit bundle of the sum of the trivial $\Bbb R$-bundle and the tautological bundle.
May 31, 2018 at 19:01 history answered mme CC BY-SA 4.0