Riemannian Geometry of G₂-type Real Flag Manifolds

2024/01/05 by Brian Grajales, Grajales, Brian, Gabriel Rondón +3
Mathematics · Medicine · Physics and Astronomy · #22F30 #53C30 #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2401.02805

openalex publication_date 2024/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate homogeneous Riemannian geometry on real flag manifolds of the split real form of \mathfrakg₂. We characterize the metrics that are invariant under the action of a maximal compact subgroup of G₂. Our exploration encompasses the analysis of g.o. metrics and equigeodesics on the \mathfrakg₂-type flag manifolds. Additionally, we explore the Ricci flow for the case where the isotropy representation has no equivalent summands, employing techniques from the qualitative theory of dynamical systems.

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