New Geometry with All Killing Vectors Spanning the Poincar\'e Algebra

The new 4D geometry whose Killing vectors span the Poincar'e algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincar'e-invariant solution of the degenerate extension of the vacuum Einstein field equations with a negative cosmological constant and provides a static cosmological space-time with a Lobachevsky space. The motion of free particles in the space-time is discussed.