Remarks on The Topology of Lorentzian Manifolds
Commun. Korean Math. Soc. 2000 Vol. 15, No. 4, 641-648
Young Suk Choi, Young Jin Suh
Kyungpook National University, Kyungpook National University
Abstract : The purpose of this paper is to give a necessary and sufficient condition for a smooth manifold to admit a Lorentzian metric. As an application of this result, on {\it Lorentzian manifolds} we have shown that the existence of a $1$-dimensional distribution is equivalent to the existence of a non-vanishing vector field.
Keywords : Lorentzian manifold, Riemannian metric, $1$-dimensional distribution, non-vanishing vector field
MSC numbers : Primary 53C50; Secondary 53C55, 53C56
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