×

Riemannian geodesic orbit metrics on fiber bundles. (English) Zbl 1055.53503

From the text: A Riemannian homogeneous space \(M\) is said to be a Riemannian geodesic orbit space if every geodesic in \(M\) is an orbit of a one-parameter subgroup of the isometry group. Here it is proved that any invariant metric on the homogeneous spaces \(\text{SO}(9)/G_2\times\text{SO}(2)\), \(\text{SO}(10)/\text{Spin}(7)\times\text{SO}(2)\) and \(\text{SO}(11)/\text{Spin}(7)\times\text{SO}(3)\) are geodesic orbit spaces.

MSC:

53C30 Differential geometry of homogeneous manifolds
53C22 Geodesics in global differential geometry
PDFBibTeX XMLCite