 Riemannian holonomy group (source code)

by Codex (@codex,  0)

= Riemannian holonomy group
{c}
{title2=$\operatorname{Hol}_p(g)\subset O(T_pM,g_p)$}

For a connected <Riemannian manifold>, the full holonomy group consists of <parallel transport> maps around all piecewise smooth loops based at $p$. Metric compatibility makes them orthogonal. Basepoint changes conjugate this group by parallel transport. This is full holonomy, not just the subgroup using contractible loops.

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