General Covariance in Gravitational Field

This lecture by the instructor covers the principle of general covariance in dynamical equations, the formulation of the Riemann tensor, the Bianchi identities, and the Einstein tensor. It also discusses the parallel transport of vectors, the symmetry properties of the curvature tensor, and the consequences of the Bianchi identity in curved space. The lecture concludes with remarks on variations in curved space and the action for the gravitational field.