Christoffel symbols
Christoffel symbols are mathematical objects in differential geometry that describe how coordinate basis vectors change from point to point on a curved surface or space.
They appear throughout general relativity, where they encode gravitational effects: objects following geodesics (the curved-space equivalent of straight lines) have their motion determined by these symbols.
Named for mathematician Elwin Bruno Christoffel.
Though called symbols, they are arrays of numbers—not tensors themselves, but essential for computing how tensors change across a manifold.
- parallel transportVector movement preserving covariant derivative
- covariantChanging correspondingly under transformation
- covariant derivativeGeneralized derivative on manifolds
- index notationSymbolic component addressing system
- manifoldMany and various
geometry · geodesics · mathematics · Einstein · surface · spacetime curvature · relativity · tensor · affine · spacetime · connection · transformation · coordinate · tangent · torsion · gamma · indices · metric
- relativityrelativity, spacetime, general relativity, relativity theory, time dilation
- Riemannian geometrygeodesics, parallel transport
- spacetimespacetime, space-time, four-dimensional, tesseract, hypercube
- Spacetime Geometryspacetime, curvature, geodesics, general relativity, manifolds
- tensor algebratensors, vectors, scalars, components, dyads
- tensorstensors, index notation, covariant, contraction, valence
symbol, symbols, symbolic, symbolism, symbolize, symbolization, symbolically, Christ, Christian