Holonomy is a general geometrical consequence of the curvature of the connection. For flat connections, the associated holonomy is a type of monodromy and is an inherently global …

Mar 11, 2021 · Holonomy, and its close cousin monodromy, is what happens when you follow a long path where each step you take produces only a little change, but when you loop back to …

3 days ago · A generic Riemannian metric on an orientable manifold has holonomy group , but for some special metrics it can be a subgroup, in which case the manifold is said to have special …

Jun 17, 2021 · The holonomy group completely determines the existence (or non-existence) of parallel vector fields, parallel differential forms, parallel spinor fields, etc. This is sometimes …

Mar 26, 2025 · Holonomy might sound like a complex term, but it's a fascinating concept in mathematics and physics. Holonomy refers to how much a vector changes when it is parallel …

One could ask how to determine, from a holonomy perspective, which elements of hom(p1(X), G)/G are associated to P under the above construction. This is addressed in various settings …

Oct 19, 2020 · This is the holonomy of ∇ around γ. Fixing a connection ∇ and a point x ∈ X the collection of all elements hol ∇ (γ) for all loops γ based at x forms a subgroup of G, called the …

May 28, 2025 · Holonomy is a fundamental concept in differential geometry that describes the parallel transport of vectors around a closed loop. To understand holonomy, we must first …

In differential geometry, the holonomy of a connection on a smooth manifold is a general geometrical consequence of the curvature of the connection measuring the extent to which …

Holonomy is a prime example of mathematical intuition and creativity - it generalises our school knowledge about the sum of angles in a triangle and led to `Berger’s holonomy theorem’ from …