Grassmann geometries on compact symmetric spaces (Q2752846)

In the article at hand, the author mainly reviews his own results on so-called \(O\)-geometries, as published in several other papers. NEWLINENEWLINENEWLINELet \(M\) be a compact simply connected Riemannian symmetric space and denote by \(G\) the identity component of the isometry group. For some \(1\leq s \leq n\), let \(G^s(T_pM)\) denote the Grassmanian of all \(s\)-dimensional linear subspaces of \(T_pM\) and \(G^s(TM)\) the Grassmann bundle over \(M\) with fibers \(G^s(T_pM)\), \(p\in M\). By definition, an \(O\)-geometry is a \(G\)-orbit in \(G^s(TM)\). Typical examples are equivariant submanifolds.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00035].