In differential geometry, the holonomy of a connection on a smooth manifold is the extent to which parallel transport around closed loops fails to preserve...

complex structure. M {\displaystyle M} has a Kähler metric with global holonomy contained in S U ( n ) {\displaystyle SU(n)} . These conditions imply that...

classification of Riemannian holonomy groups first raised the issue of the existence of non-symmetric manifolds with holonomy Sp(n)·Sp(1). Interesting results...

manifold or Joyce manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G 2 {\displaystyle G_{2}} is one of the...

restricted holonomy group is contained in the symplectic group. A G2 manifold or Spin(7) manifold is a Riemannian manifold whose holonomy group is contained...

Look up holonomic or holonomy in Wiktionary, the free dictionary. Holonomic (introduced by Heinrich Hertz in 1894 from the Greek ὅλος meaning "whole",...

phenomenon is known as holonomy. Various generalizations capture in an abstract form this idea of curvature as a measure of holonomy; see curvature form...

of Bertram Kostant, gave a new proof of Berger's classification of the holonomy groups of Riemannian manifolds. He subsequently began to work with Shiing-Shen...

within the larger workings of the brain. This patch holography is called holonomy or windowed Fourier transformations. A holographic model can also account...

possible special groups that can appear as the holonomy group of a Riemannian metric. The manifolds of G2 holonomy are also called G2-manifolds. G2 is the automorphism...

a Spin(7)-manifold is an eight-dimensional Riemannian manifold whose holonomy group is contained in Spin(7). Spin(7)-manifolds are Ricci-flat and admit...

Compact Manifolds with special holonomy. Oxford University Press. 2000. ISBN 978-0-19-850601-0. Riemannian holonomy groups and calibrated geometry. Oxford...

tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete...

a Riemannian product automatically implies a product structure of the holonomy groups. In 1952 De Rham considered the converse, proving that, if there...

gauge theories and quantum gravity. LQG includes the concept of a holonomy. A holonomy is a measure of how much the initial and final values of a spinor...

to x {\displaystyle x} . Parallel transport can be used to define the holonomy group of the connection ∇ {\displaystyle \nabla } based at a point x {\displaystyle...

is called the holonomy of the foliation. Holonomy is implemented on foliated manifolds in various specific ways: the total holonomy group of foliated...

gauge theories in terms of extended objects such as Wilson loops and holonomies. The loop representation is a quantum hamiltonian representation of gauge...

closed manifolds of special holonomy; any simply-connected closed Kähler manifold which is Ricci flat must have its holonomy group contained in the special...

quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(n)·Sp(1) for some n ≥ 2 {\displaystyle n\geq...

theory concerns itself primarily with notions of parallel transport and holonomy. The infinitesimal theory concerns itself with the differentiation of geometric...

the curvature known as holonomy. The Ambrose–Singer theorem makes explicit this relationship between the curvature and holonomy. Other notions of connection...

 [page needed], Vol. 1. Holonomy for Ehresmann connections in fiber bundles is sometimes called the Ehresmann-Reeb holonomy or leaf holonomy in reference to the...

contributions to differential geometry, in particular manifolds with special holonomy and on non-integrable geometric structures and for service to the mathematical...

It is the only closed flat 3-manifold with first Betti number zero. Its holonomy group is Z 2 2 {\displaystyle \mathbb {Z} _{2}^{2}} . It has been suggested...

path-ordered exponential to guarantee that the Wilson loop encodes the holonomy of the gauge connection. The parameter σ that determines the ordering is...

weaker than the existence of a metric of holonomy G 2 {\displaystyle G_{2}} , because a compact 7-manifold of holonomy G 2 {\displaystyle G_{2}} must also...

observed that since the Yang–Mills connections are projectively flat, their holonomy gives projective unitary representations of the fundamental group of the...

exceptional holonomy (i.e. whose holonomy groups are G2 or Spin(7)); this showed that every group in Marcel Berger's classification can arise as a holonomy group...

(principal bundle) Ehresmann connection curvature curvature form holonomy, local holonomy Chern–Weil homomorphism Curvature vector Curvature form Curvature...