Abstract
This chapter provides an introduction to the Riemannian or pseudo-Riemannian manifolds (M,g) of finite dimension m. It defines the notion of geodesic form for a pseudo-Riemannian manifold of constant sectional curvature and presents the proofs of some of its main properties. The chapter further discusses a spinor calculus. The Levi-Civita spinor field allows the transition from contravariant spinors to covariant spinors and vice versa. This is the process of raising and lowering the indices. The structure of tensor equations becomes more transparent if they are translated in the spinor language. There are many identities between the coordinates of the Weyl tensor. Some of them are linear, quadratic, and cubic. These identities are obvious if they are written in spinor language.
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