Polars and antipodal sets of generalized $s$-manifolds

TL;DR

This paper introduces generalized s-manifolds, extending symmetric spaces, and explores their polars and antipodal sets to generalize results from compact symmetric spaces.

Contribution

It defines generalized s-manifolds, provides a construction method, and studies their polars and antipodal sets to extend classical symmetric space results.

Findings

Construction method for generalized s-manifolds

Examples of generalized s-manifolds

Extension of polars and antipodal set results

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.