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THE UNCONNECTED MANIFOLD
Integrals Densities Derivatives
AFFINELY CONNECTED MANIFOLD
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affine connexion antisymmetric tensor arbitrary array called Chapter Christoffel brackets coefficients computation conservation laws constant continuum contravariant vector density convention coordinates course covariant vector curve definite determinant differential Einstein-tensor Einstein's Einstein's field equations elementary envisage example expression fact field equations four four-dimensional frame functions fundamental tensor geodesic geometrical given gravitational field Hamiltonian derivatives Hence hold identities independent components indices inertial infinitesimal integrable affinity integrand invariant derivative line-element linear aggregates linear transformation Lorentz-transformation matter meaning metric metrical tensor momentum neighbouring point non-symmetric affinity notation notion obtain parallel-transfer particle point-events quantities refer regard respect restricted scalar density second rank semicolon Sgik simple skew tensor space-time Special Relativity star affinity subscripts summation symmetric affinity symmetrical tensor tensor density tensor gik theorem theory Theory of Relativity tion Tklm transformation formula vanish variational principle vector-field velocity world-point zero zero tensor