Completeness of compact Lorentz manifolds admitting a timelike conformal Killing vector field
نویسندگان
چکیده
منابع مشابه
Completeness of Compact Lorentz Manifolds Admitting a Timelike Conformal Killing Vector Field
It is proved that every compact Lorentz manifold admitting a timelike conformai Killing vector field is geodesically complete. So, a recent result by Kamishima in J. Differential Geometry [37 (1993), 569-601] is widely extended. Recently, it has been proved in [2] that a compact Lorentz manifold of constant curvature admitting a timelike Killing vector field is (geodesically) complete. It is na...
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We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is never vanishing, then there are at least two distinct periodic geodesics; as ...
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Lorentzian manifolds admitting a Killing vector field have been studied in the literature from different points of view. Functional analysis, proper actions of Lie groups or Bochner’s technique in Differential Geometry, have been some of the very different tools involved to study them. The purpose of this paper is to review some of their properties, pointing out several techniques and supplying...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1995-1257122-3