Invariant Affine Connections on Homogeneous Spaces

1954/01/01 by Katsumi Nomizu · 536 citations
Mathematics · #Affine transformation #Combinatorics #Homogeneous #Invariant (physics) #Mathematical physics #Mathematics #Pure mathematics #advanced mathematical theories

paper · open access · doi:10.2307/2372398

published in American Journal of Mathematics 76(1), 33 (Johns Hopkins University Press)

openalex publication_date 1954/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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• Reductive homogeneous spaces associated with real forms. A gauge-theoretical generalisation
• Associative-Yamaguti algebras
• Optimal Remainder Estimates in the Quantization of Complex Projective Spaces
• Remarks on the geometry of the extended Siegel--Jacobi upper half-plane
• A characterization of the alpha-connections on the statistical manifold of normal distributions
• Isoclinism in regular Hom-Lie Yamaguti algebras
• Conical Distributions on the Space of Flat Horocycles
• Sasakian structures on tangent sphere bundles of compact rank-one symmetric spaces
• The Ambrose-Singer Theorem for general homogeneous manifolds with applications to symplectic geometry
• G2 geometry and integrable systems
• Invariant metric f-structures on specific homogeneous reductive spaces
• Some invariant connections on symplectic reductive homogeneous spaces
• Atiyah constructions for Lie algebroid connections on fiber bundles
• The Geometry of Extended Kalman Filters on Manifolds with Affine Connection
• Universal Coacting Hopf algebra of a Finite dimensional Lie-Yamaguti algebra
• Einstein Homogeneous Riemannian Fibrations
• Representations and deformations of Hom-Lie-Yamaguti superalgebras
• A twisted generalization of Lie-Yamaguti algebras
• Realization of coherent state Lie algebras by differential operators
• The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras
• Compact Homogeneous Riemannian Manifolds with Strictly Positive Curvature
• Quantization of formal classical dynamical r-matrices: the reductive case
• Geodesic Flows on Symmetric Riemann Spaces
• Theory of connections
• Topology of quaternionic manifolds
• Homogenisation on homogeneous spaces
• Topology of quaternionic manifolds
• Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
• On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
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• Nonlinear wave superpositions and quasi-rectifiable Lie modules
• Balanced Metric and Berezin Quantization on the Siegel-Jacobi Ball
• Invariant Poisson Structures on Homogeneous Manifolds: Algebraic Characterization, Symplectic Foliation, and Contravariant Connections
• Symmetric space [wikipedia]
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