Abstract
Publisher Summary This chapter discusses the research on four relevant topics on Lorentzian geometry. Several Lorentzian results are compared to Riemannian or indefinite (non-Lorentzian) ones, emphasizing on mathematical behaviors, which are specific of Lorentzian geometry. Degenerate tangent planes play an important role in the study of the geometry of Lorentzian manifolds. Harris introduced the notion of null sectional curvature for degenerate tangent planes, which has shown to be fruitful to get some comparison theorems and to characterize Robertson–Walker spacetimes. The chapter discusses Bochner technique on Lorentzian manifolds focusing aims and difficulties.
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