Homogeneous spaces of curvature bounded below (Q1589344)

The authors study the geometry of homogeneous spaces with certain restrictions concerning its curvature. Ten theorems are proved. In particular, each normal homogeneous space has non-negative curvature and every minimal curve in it extends to a geodesic which is the orbit of a one-parameter group of isometries. Also, each locally compact group with bi-invariant inner metric of curvature bounded below is a direct product of a compact group with bi-invariant metric of non-negative curvature and a finite dimensional vector space. A metric space admits transitive group of Wolf translations iff it is isometric to a group with bi-invariant metric.