Riemannian geometry of $G_2$-type real flag manifolds

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发表日期：

2025年8月7日

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Brian Grajales,
Gabriel Rondón,
Julieth Saavedra

摘要

We investigate homogeneous Riemannian geometry on real flag manifolds of the split real form of ${\mathfrak {g}}_2$ $g_{2}$ and characterize the metrics that are invariant under the action of a maximal compact subgroup of $G_2$ $G_{2}$ . Our exploration encompasses the analysis of geodesic orbit metrics and equigeodesics on the ${\mathfrak {g}}_2$ $g_{2}$ -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.

Riemannian geometry of \(G_2\)-type real flag manifolds

摘要