holonomy
1Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… …
2holonomy — noun Given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to… …
3Calabi–Yau manifold — In mathematics, Calabi ndash;Yau manifolds are compact Kähler manifolds whose canonical bundle is trivial. They were named Calabi ndash;Yau spaces by physicists in 1985, [cite journal | author = Candelas, Horowitz, Strominger and Witten | year =… …
4G2 manifold — A G 2 manifold is a seven dimensional Riemannian manifold with holonomy group G 2. The group G 2 is one of the five exceptional simple Lie groups. It can be described as the automorphism group of the octonions, or equivalently, as a proper… …
5Ehresmann connection — In differential geometry, an Ehresmann connection (after the French mathematician Charles Ehresmann who first formalized this concept) is a version of the notion of a connection which is defined on arbitrary fibre bundles. In particular, it may… …
6Magnetic monopole — It is impossible to make magnetic monopoles from a bar magnet. If a bar magnet is cut in half, it is not the case that one half has the north pole and the other half has the south pole. Inst …
7Connection (vector bundle) — This article is about connections on vector bundles. See connection (mathematics) for other types of connections in mathematics. In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; …
8Quaternion-Kähler manifold — In differential geometry, a quaternion Kähler manifold (or quaternionic Kähler manifold) is a Riemannian manifold whose Riemannian holonomy group is a subgroup of Sp( n )·Sp(1). Another, more explicit, definition, uses a 3 dimensional subbundle H …
9Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …
10Parallel transport — In geometry, parallel transport is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection (a covariant derivative or connection on the tangent bundle), then this connection… …
