Structure of geodesics in a 13-dimensional group of Heisenberg type (Q2733932)

A \(g.o.\) space is a homogeneous Riemannian manifold \((G/H, g)\) with the property that every geodesic is an orbit of a one-parameter subgroup of \(G\). A naturally reductive space is a homogeneous space \((G/H,g)\) with the property that there exists a complement \({\mathcal M}\) to the Lie algebra \({\mathcal H}\) of \(H\) such that the one-parameter group generated by every nonzero element from \({\mathcal M}\) defines a geodesic in \(G/H\). The \(g.o.\) spaces can be characterized by the degree of the geodesic graph which is a rational map: \({\mathcal M}\to {\mathcal H}\). The author studies the generalized 13-dimensional Heisenberg group with 5-dimensional center, thought of as a \(g.o.\) space for which the degree of the canonical geodesic graph is six.NEWLINENEWLINEFor the entire collection see [Zbl 0966.00031].