Stability of certain reflective submanifolds in compact symmetric spaces (Q1002475)

\textit{J. Berndt} and \textit{H. Tamaru} [Tohoku Math. J., II. Ser. 56, No. 2, 163--177 (2004; Zbl 1066.53097)] have classified cohomogeneity one actions on irreducible Riemannian symmetric spaces of noncompact type with a totally geodesic singular orbit and established a duality principle between noncompact and compact type. By using their results and a formula of \textit{M. Takeuchi} [Tôhoku Math. J., II. Ser. 36, 293--314 (1984; Zbl 0528.53047)] regarding the index of a totally geodesic embedding, the author of this paper determines exactly which ones of the totally geodesic singular orbits of cohomogeneity one actions on compact simply-connected irreducible symmetric spaces are stable.