On the automorphism group of the generalized conformal structure of a symmetric \(R\)-space
Let \(g=g_{-1}\oplus g_{0}\oplus g_{1}\) be a simple graded Lie algebra and \(G_{0}\) the group of grade-preserving automorphisms. Then \(G=G_{0}\cdot \text{Inn}(g)\) is an open subgroup of \(\Aut(g)\) and \(U=G_{0}\cdot \exp(g_{1})\) is a subgroup in \(G\). The coset space \(M=G/U\) is called a symmetric \(R\)-space associated with \(g\). These spaces were introduced by \textit{T. Nagano} [Trans. Am. Math. Soc. 118, 428-453 (1965; Zbl 0151.28801)] and \textit{M. Takeuchi} [J. Fac. Sci., Univ. Tokyo, Sect. I 12, 81-191 (1965; Zbl 0144.22804)]. The authors define a generalized conformal structure \(\mathcal K\) on a symmetric \(R\)-space of rank greater than 1. It is a smooth assignment of a cone \(V_{p}\) in each tangent space \(T_{p}M\). A smooth map \(f\) is said to be conformal with respect to \(\mathcal K\) if \(df(V_{p})=V_{f(p)}\) for each \(p\in M\). The group of all \(\mathcal K\)-conformal automorphisms of \(M\) coincides with \(G\).
scientific article; zbMATH DE number 1145932
scientific article