A new class of weakly symmetric spaces
A Riemannian manifold \(M\) is called weakly symmetric if any two points \(x,y \in M\) can be interchanged by an isometry. The authors prove that a simply connected Riemannian manifold \(M\) is weakly symmetric if it admits a complete unit Killing vector field \(X\) such that the reflections with respect to the flow lines of \(X\) can be extended to global isometries of \(M\). In the case when the orthogonal complement to \(X\) is a contact distribution, the orbit space of the 1-parameter group of isometries of \(M\) generated by \(X\) is a Hermitian symmetric space.
scientific article; zbMATH DE number 1439639
scientific article