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...

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

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

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",...

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

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

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...

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

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

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

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...

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

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

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

Zeiger (1967) proved an important variant called the holonomy decomposition (Eilenberg 1976). The holonomy method appears to be relatively efficient and has...

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...

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

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

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...

March 2009). "Electromagnetic to Gravitational wave Conversion via Nuclear Holonomy". AIP Conference Proceedings. 1103 (1): 524–531. Bibcode:2009AIPC.1103...

Bryant, Robert L. (2006). "Geometry of manifolds with special holonomy: '100 years of holonomy'". 150 years of mathematics at Washington University in St...

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...

Euclidean (ALE) metric on the cotangent bundle of the 2-sphere T*S2. The holonomy group of this 4-real-dimensional manifold is SU(2). The metric is generally...

strongly scalar-flat, M must be a product of Riemannian manifolds with holonomy group SU(n) (Calabi–Yau manifolds), Sp(n) (hyperkähler manifolds), or Spin(7)...

automorphism group Level structure, a technique to remove an automorphism group Holonomy group First, if G is simply connected, the automorphism group of G is that...

everywhere future-directed null (or everywhere past-directed null). The holonomy of the ratio of the rate of change of the affine parameter around a closed...

Bryant, Robert L. (2006). "Geometry of manifolds with special holonomy: '100 years of holonomy'". 150 years of mathematics at Washington University in St...

quantum general relativity and in turn loop quantum gravity and quantum holonomy theory. Let us introduce a set of three vector fields   E j a   , {\displaystyle...