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What is Cartan Connection and Riemannian Curvature about?

This document defines connections and curvature on Riemannian manifolds. It begins by defining an affine connection on a vector bundle and the Levi-Civita connection on the tangent bundle of a Riemannian manifold. It then introduces the Riemann curvature tensor as a measure of the failure of covariant derivatives to commute. Explicit formulas are given for the Christoffel symbols, Riemann curvature tensor, and its components in local coordinates. The document aims to generalize the notion of Riemannian curv

Author

Luca Selva Campobasso

Language

EN