Codazzi tensor fields in reductive homogeneous spaces

2023/06/12 by James Marshall Reber, Ivo Terek, Reber, James Marshall +1 · 1 citation
Mathematics · Physics and Astronomy · #53C30 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2306.07444

openalex publication_date 2023/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the results about left-invariant Codazzi tensor fields on Lie groups equipped with left-invariant Riemannian metrics obtained by d'Atri in 1985 to the setting of reductive homogeneous spaces G/H, where the curvature of the canonical connection of second kind associated with the fixed reductive decomposition \mathfrakg = \mathfrakh⊕\mathfrakm enters the picture. In particular, we show that invariant Codazzi tensor fields on a naturally reductive homogeneous space are parallel.

Cited by

• Self-Reconstructing Codazzi Defects, \mathbbCP¹ Quantization, and the Minimal Standard-Model Carrier

Related

• Parallel Codazzi tensors with submanifold applications
• Covariant Derivatives on Homogeneous Spaces -- Horizontal Lifts and Parallel Transport
• Left-invariant Codazzi tensors and harmonic curvature on Lie groups endowed with a left invariant Lorentzian metric
• Some invariant connections on symplectic reductive homogeneous spaces
• Codazzi Tensors with Two Eigenvalue Functions