A survey on natural Γ-symmetric structures on 𝑅-spaces

Abstract

This is a report upon the authors’ 2020 paper on Γ \Gamma -symmetric structures on R R -spaces, which continues various aspects of Nagano’s work. We first briefly recall some generalizations of symmetric spaces. Next we show that certain R R -spaces admit Γ \Gamma -symmetric structures appearing in a natural way as a generalization of symmetric R R -spaces. Moreover we describe the maximal antipodal sets of these natural Γ \Gamma -symmetric structures.