Let $X$ be a Riemannian manifold and $TX$ its tangent bundle. Is there a name for the $S^1$-bundle given by the unit length tangent vectors?
2026-03-29 11:13:36.1774782816
Unit length tangent vectors on a Riemannian manifold
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This is only an $S^1$-bundle when $X$ is a surface. In general it's called the sphere bundle of $X$ or unit tangent bundle and is an $S^{n-1}$-bundle when $\dim X = n$. :)