Let $M$ be a manifold and $Q\subseteq M$ a submanifold. Suppose that there is an integrable distribution (sub-bundle) $E$ of $TM|_Q$ such that $TM|_Q=TQ\bigoplus E$. Can we guarantee a (Riemannian) metric $g$ on $M$ such that $E=TQ^\perp$?
2026-03-25 23:09:00.1774480140
Metric that makes distribution orthogonal to each other
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