Lorentz Manifolds And Its Isoparametric Hypersurfaces

In the thesis, there are three parts to introduce our work in Lorentz manifold.In the first part, the research background of this thesis, as well as the preliminary knowledge and fundamental lemmas are introduced.In the second part, by comparison with the Riemann manifold, an important conclusion is drawn, that is, in a Lorentz manifold, the curvature tensor R of Levi-Civita connection on the g is anti symmetric. Moreover, the necessary and sufficient condition of Einstein tensor G=0is Ric=0.In the third part, the definition, formula and theorem of the isopara-metric hypersurface in the Ln+1space, Hn1+1space and Sn1+1space are described in details.