Weakly reflective submanifolds and austere submanifolds

2006/12/14 by Osamu Ikawa, Ikawa, Osamu, Takashi Sakai +3 · 2 citations
Mathematics · Physics and Astronomy · #53C35 (Secondary) #53C40 (Primary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C35 #msc:53C40

paper · pdf · doi:10.48550/arxiv.math/0612384

30 pages

arxiv created 2006/12/14 · openalex publication_date 2006/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of s-representations.

Citations

• Calibrated geometries

Cited by

• Compact symmetric triads and symmetric triads with multiplicities
• On cohomogeneity one hyperpolar actions related to G₂

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