  The Lie group SO_0(n, 1) has the left-invariant metric coming from the
Killing-Cartan form. The maximal compact subgroup SO(n) of the isometry group
acts from the left. The geometry of the quotient space of the homogeneous
submersion SO_0(n, 1) -> SO(n)\SO_0(n, 1) is investigated. The space is
expressed as a warped product. Its group of isometries and sectional curvatures
are calculated.
