A note on the uniqueness of the canonical connection of a naturally reductive space

DOI10.1007/s00605-013-0554-6zbMath1296.53106arXiv1210.8374OpenAlexW2108567313MaRDI QIDQ387548

Silvio Reggiani, Carlos E. Olmos

Publication date: 23 December 2013

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.8374

zbMATH Keywords

isometry groupcanonical connectionnaturally reductive spacesskew-symmetric torsion

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Differential geometry of symmetric spaces (53C35) Connections (general theory) (53C05)

Related Items (8)

Tangent Lie groups are Riemannian naturally reductive spaces ⋮ Invariant connections and \(\nabla\)-Einstein structures on isotropy irreducible spaces ⋮ Structure theory of naturally reductive spaces ⋮ \(S^6\) and the geometry of nearly Kähler 6-manifolds ⋮ Jacobi relations on naturally reductive spaces ⋮ Compact homogeneous Riemannian manifolds with low coindex of symmetry ⋮ The index of symmetry of compact naturally reductive spaces ⋮ Submanifolds, holonomy, and homogeneous geometry

Cites Work

• On the transitivity of holonomy systems
• On isotropy irreducible Riemannian manifolds
• On the affine group of a normal homogeneous manifold
• On the holonomy of connections with skew-symmetric torsion
• The geometry and structure of isotropy irreducible homogeneous spaces
• The skew-torsion holonomy theorem and naturally reductive spaces
• Isometry groups of homogeneous spaces with positive sectional curvature
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