Abstract
Abstract This chapter surveys some results concerning symmetry and spaces of constant curvature. It begins with a review of Riemannian curvature, sectional curvature, and the relation between them, before turning to highly symmetric Riemannian and Lorentz spaces of constant sectional curvature. The primary goal is to equip readers with concepts and results that will play a role in later chapters. Another goal is to place de Sitter spacetime in context: a theme of this chapter is that de Sitter spacetime has a near relative, elliptic de Sitter spacetime, that is in several senses its rival-each has a claim to be the most natural general relativistic geometry in the context of a positive cosmological constant.
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