98 research outputs found
Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application
In this article we extend the Gallot-Tanno theorem to closed
pseudo-Riemannian manifolds. It is done by showing that if the cone over such a
manifold admits a parallel symmetric 2-tensor then it is incomplete and has non
zero constant curvature. An application of this result to the existence of
metrics with distinct Levi-Civita connections but having the same
unparametrized geodesics is given
Feuilletages totalement géodésiques, flots riemanniens et variétés de Seifert
International audienc
Pseudo-Riemannian geodesic foliations by circles
We investigate under which assumptions an orientable pseudo-Riemannian
geodesic foliations by circles is generated by an -action. We construct
examples showing that, contrary to the Riemannian case, it is not always true.
However, we prove that such an action always exists when the foliation does not
contain lightlike leaves, i.e. a pseudo-Riemannian Wadsley's Theorem. As an
application, we show that every Lorentzian surface all of whose
spacelike/timelike geodesics are closed, is finitely covered by .
It follows that every Lorentzian surface contains a non-closed geodesic.Comment: 14 page
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