Some differential-geometric properties of \(R\)-spaces
An \(R\)-space is the orbit \(Ad(K)a\) of a point \(a\) belonging to the unit hypersphere \(S\) of \(T_0(G/K)\), where \(G/K\) is an irreducible Riemannian symmetric space and \(Ad(K)\) the adjoint representation group. \(R\)-spaces form a large class of homogeneous Riemannian manifolds. In the paper under review, new examples of homogeneous CR-submanifolds of a complex projective space are given, after investigating the relations between the complex structure and the restricted root system when \(G/K\) is Hermitian. Moreover, it is proved, through the expression of the covariant derivative of the second fundamental form of an \(R\)-sapce, that a cyclic-parallel \(R\)-space is necessarily parallel.
scientific article; zbMATH DE number 1822086