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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