A geometric proof of the Berger Holonomy Theorem

2005/01/01 by Carlos Olmos · 46 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Euclidean geometry #Geometric Analysis and Curvature Flows #Geometry #Holonomy #Mathematical analysis #Mathematics #Pure mathematics #Submanifold

paper · pdf · doi:10.4007/annals.2005.161.579

published in Annals of Mathematics 161(1), 579-588 (Princeton University)

openalex publication_date 2005/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/21

Abstract

We give a geometric proof of the Berger Holonomy Theorem. The proof uses Euclidean submanifold geometry of orbits and gives a link between Riemannian holonomy groups and normal holonomy groups.

Citations

• Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
• On the Transitivity of Holonomy Systems

Cited by

• Geometric Obstructions on Gravity
• On the nullity distribution of the second fundamental form of a submanifold of a space form
• Holonomy [wikipedia]