On cohomogeneity one hyperpolar actions related to G₂

2025/04/16 by Shinji Ohno, Ohno, Shinji, Yuuki Sasaki +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2504.11766

Abstract

Cohomogeneity one actions on irreducible Riemannian symmetric spaces of compact type are classified into three cases: Hermann actions, actions induced by the linear isotropy representation of a Riemannian symmetric space of rank 2, and exceptional actions. In this paper, we consider exceptional actions related to the exceptional compact Lie group G₂ and investigate some properties of their orbits as Riemannian submanifolds. In particular, we examine the principal curvatures of principal orbits and classify principal orbits that are minimal, austere, weakly reflective, and proper biharmonic.

Related

• Cohomogeneity one actions on some noncompact symmetric spaces of rank two
• Cohomogeneity one actions on symmetric spaces of noncompact type
• Hyperpolar actions on reducible symmetric spaces
• Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups
• Curvatures and austere property of orbits of path group actions induced by Hermann actions