# Index

**Next:** About this document **Up:** Title page ** Previous:** The Einstein Tensor

**basis, orthonormal**

**Bianchi identities**

**Bianchi identities, contracted**

**Christoffel symbols**

**Christoffel symbols, symmetry of**

**Christoffel symbols, from the metric**

**Christoffel symbols, in polar coordinates**

**comma goes to semicolon rule**

**covariant derivative, of a one- form**

**covariant derivative**

**covariant derivative, commutator of**

**covariant derivative, of a vector**

**curvature**

**curvature, extrinsic**

**curvature, intrinsic**

**curvature, of a cylinder**

**curvature, of a sphere or balloon**

**Einstein tensor, definition of**

**equivalence principle**

**equivalence principle**

**Euclidian space** ,

**Euler- Lagrange equations**

**geodesic**

**geodesic, as equation of motion for a free particle**

**geodesic, calculating for a given metric**

**geodesic, definition of**

**geodesic, extremal length of**

**geodesic deviation**

**geodesic deviation, equation of**

**geodesic equation**

**geodesics**

**inertial frame, local**

**Lagrangian, for timelike curves**

**local flatness theorem**

**manifold**

**manifold, differentiable**

**manifold, dimension of**

**manifold, Riemannian**

**metric, as a mapping**

**metric, as gravitational potentials**

**metric, connection**

**metric, signature of**

**Newtonian gravity**

**one- form**

**one- form, basis in polar coordinates**

**parallel transport**

**parallel transport, around a loop, in flat space**

**parallel transport, definition of**

**parallel transport, around a loop, in curved space**

**polar coordinates, tensors in**

**polar coordinates, vector gradient in**

**proper time, for curved spacetime**

**proper time, for flat spacetime**

**Pseudo- Riemannian**

**Ricci scalar, definition of**

**Ricci tensor, definition of**

**Riemann tensor, definition of**

**Riemann tensor, in a local inertial frame**

**Riemann tensor, number of independent components of**

**Riemann tensor, symmetries of**

**Special Relativity**

**tensor**

**tensor, curvature**

**transformation, of Christoffel Symbols**

**vector**

**vector, basis in polar coordinates**

**worldlines**