BOOK-CHAPTER
Riemannian Holonomy Groups
Abstract
Abstract Let M be a manifold, and g a Riemannian metric on M . Then there is a unique, preferred connection ∇ on TM called the Levi-Civita connection, which is torsion-free and satisfies ∇g = ∇0. The curvature R(∇) of the Levi-Civita connection is called the Riemann curvature, and its holonomy group Hol(∇) the Riemannian holonomy group Hol(g) of g.
Keywords:
Holonomy Connection (principal bundle) Levi-Civita connection Metric connection Mathematics Pure mathematics Torsion (gastropod) Curvature Sectional curvature HOL Group (periodic table) Exponential map (Riemannian geometry) Riemann curvature tensor Riemannian manifold Metric (unit) Fundamental theorem of Riemannian geometry Topology (electrical circuits) Mathematical analysis Ricci curvature Physics Geometry Combinatorics Scalar curvature Quantum mechanics
Metrics
0
Cited By
0.00
FWCI (Field Weighted Citation Impact)
0
Refs
0.61
Citation Normalized Percentile
Is in top 1%
Is in top 10%
Topics
Advanced Differential Geometry Research
Physical Sciences → Physics and Astronomy → Astronomy and Astrophysics
Geometric Analysis and Curvature Flows
Physical Sciences → Mathematics → Applied Mathematics
Geometry and complex manifolds
Physical Sciences → Mathematics → Geometry and Topology
Related Documents
BOOK-CHAPTER
Riemannian Holonomy Groups and Exceptional Holonomy
Encyclopedia of Mathematical Physics Year: 2006 Pages: 441-446
JOURNAL ARTICLE
Riemannian geometry and holonomy groups
Journal: Acta Applicandae Mathematicae Year: 1990 Vol: 20 (3)Pages: 309-311