Retrieving "Harmonic Representative" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Riemannian Manifold

   Linked via "harmonic representatives"

   Parallel transport is the process of moving a vector field along a curve such that its covariant derivative along the curve is zero, effectively preserving the vector relative to the local metric structure. The set of all linear transformations generated by parallel transporting vectors around all possible closed loops based at a point $p$ forms the Holonomy Group, denoted $\text{Hol}(M, p)$. The structure of the holonomy group re…