Foliation of a dynamically homogeneous neutral manifold

Abstract

It is known that Riemannian and Lorentzian four-dimensional dynamically homogeneous manifolds are two-point homogeneous spaces. This is not true for signature (--++) (neutral or Kleinian signature). In order to better understand their rich structure we study the geometry of nonsymmetric dynamically homogeneous spaces (types II and III): they admit autoparallel distributions and they are locally foliated by totally geodesic, flat, isotropic two-dimensional submanifolds. Moreover we characterize them locally in terms of the existence of an appropriate coordinate system (in the sense of A. G. Walker [Q. J. Math. 1, 69-79 (1950)]). © 1998 American Institute of Physics.