Foliation of a dynamically homogeneous neutral manifold

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...

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Veröffentlicht in:Journal of mathematical physics 1998-11, Vol.39 (11), p.6118-6124
Hauptverfasser: Blažić, Novica, Bokan, Neda, Rakić, Zoran
Format: Artikel
Sprache:eng
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Zusammenfassung: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)]).
ISSN:0022-2488
1089-7658
DOI:10.1063/1.532617