Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
curved spacetime
curved surfaces |
| gptkbp:describes |
gptkb:geometry
|
| gptkbp:expressedIn |
path of shortest distance between points on a manifold
|
| gptkbp:field |
gptkb:general_relativity
differential geometry |
| gptkbp:firstPublished |
19th century
|
| gptkbp:formedBy |
gptkb:Bernhard_Riemann
|
| https://www.w3.org/2000/01/rdf-schema#label |
geodesic equation
|
| gptkbp:involves |
gptkb:Christoffel_symbols
|
| gptkbp:mathematical_form |
second-order differential equation
|
| gptkbp:relatedConcept |
metric tensor
parallel transport affine parameter |
| gptkbp:relatedTo |
free-fall motion in general relativity
|
| gptkbp:solution_is |
geodesic curve
|
| gptkbp:symbolic_form |
d^2x^μ/dλ^2 + Γ^μ_{νσ} dx^ν/dλ dx^σ/dλ = 0
|
| gptkbp:used_in |
gptkb:Einstein_field_equations
gptkb:Riemannian_geometry pseudo-Riemannian geometry |
| gptkbp:bfsParent |
gptkb:Christoffel_symbols
gptkb:Christoffel_symbol |
| gptkbp:bfsLayer |
6
|