On the stability of Cartan embeddings of compact symmetric spaces (Q1203525)

Let \(G\) be a compact connected Lie group and \(\sigma\) be an involutive automorphism on \(G\). Then we have an embedding \(\Sigma\) of \(G/K\) into \(G\); \(\Sigma(gK)=g\sigma(g^{-1})\). The embedding \(\Sigma\) is called the Cartan embedding. It is well-known that the image of \(\Sigma\) is a totally geodesic submanifold of \(G\). The author determined whether the image \(\Sigma(G/K)\) is stable or unstable as a minimal submanifold of \(G\) under the assumption that \(G\) is a compact simple Lie group.