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The study of nontransitive actions of a Lie group G on a smooth manifold is a very interesting problem. The first and most natural case is the case when the action is of cohomogeneity one . Many mathematicians have studied cohomogeneity one Riemannian Gmanifolds and there are much nice result in the literature on the subject. But for the cohomogeneity one pseudoRiemannian manifolds there are no much result in the literature. In this book, which is based on the Ph.D. thesis of the first author, we want to study these manifolds.
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