Polars and antipodal sets of generalized s-manifolds

2025/08/16 by Ohno, Shinji, Sakai, Takashi · 1 citation
#53C35 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.11855

Abstract

In this paper, we introduce the notion of generalized s-manifolds, which is a generalization of symmetric spaces. Then we give a method to construct generalized s-manifolds and present some typical examples. We study polars and antipodal sets of generalized s-manifolds aiming to extend the results on compact symmetric spaces due to Chen and Nagano.

Citations

• The intersection of two real flag manifolds in a complex flag manifold
• On classification of periodic maps on the 2-torus
• Maximal Antipodal Sets and the Topology of Generalised Symmetric Spaces
• (Z/2Z x Z/2Z)-symmetric spaces
• A classifying invariant of knots, the knot quandle

Cited by

• Polars and antipodal sets for the outer 3-symmetric space \mathbbS⁷ × \mathbbS⁷

Related

• Natural Γ-symmetric structures on R-spaces
• Maximal Antipodal Sets and the Topology of Generalised Symmetric Spaces
• Antipodal sets of exceptional symmetric spaces
• A complete description of the antipodal set of most symmetric spaces of compact type
• Polars and antipodal sets for the outer 3-symmetric space \mathbbS⁷ × \mathbbS⁷