Is there an even integer $n$ such that $S^n$ can be embedded in its unit tangent bundle $$T^{1} S^n=\{(x,y)\in S^n \times S^n \mid x.y=0\}$$ What about if we pose the extra condition that the image of $S^n$ is a retract of the unit tangent bundle?
(retract) embedding of $S^{n}$ in its unit tangent bundle
Ali Taghavi
- 356
- 8
- 31
- 123