Statements (60)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:networking
|
| gptkbp:can_be_computed_using |
Christoffel symbols
|
| gptkbp:defined_on |
Riemannian manifold
|
| gptkbp:developed_by |
the metric tensor
the Laplace-Beltrami operator |
| gptkbp:has_natural_feature |
given a Riemannian metric
|
| https://www.w3.org/2000/01/rdf-schema#label |
Levi-Civita connection
|
| gptkbp:importance |
generalized coordinates
|
| gptkbp:is_a_crucial_concept_in |
the analysis of differential forms
|
| gptkbp:is_a_foundation_for |
modern geometry
|
| gptkbp:is_a_key_component_of |
the connection theory
the formulation of physical theories |
| gptkbp:is_analyzed_in |
geometric structures
geometric properties of manifolds |
| gptkbp:is_applicable_to |
pseudo-Riemannian manifolds
|
| gptkbp:is_associated_with |
geodesics
the notion of curvature in physics |
| gptkbp:is_compatible_with |
Riemannian metric
|
| gptkbp:is_connected_to |
gptkb:Einstein's_field_equations
the study of symplectic geometry |
| gptkbp:is_critical_for |
mathematical physics
|
| gptkbp:is_defined_by |
metric compatibility and torsion-free condition
|
| gptkbp:is_described_as |
parallel transport
differential equations on manifolds the covariant derivative |
| gptkbp:is_essential_for |
Riemannian geometry
geometric analysis geometric flows the structure of spacetime |
| gptkbp:is_essential_for_the_study_of |
geometric topology
|
| gptkbp:is_explored_in |
the properties of vector fields
|
| gptkbp:is_fundamental_to |
gptkb:Physics
the calculus of variations the theory of connections and curvature. |
| gptkbp:is_involved_in |
the study of curvature
|
| gptkbp:is_related_to |
curvature tensor
the concept of parallelism the concept of geodesic completeness the concept of affine transformations affine structures |
| gptkbp:is_significant_for |
the study of manifolds
|
| gptkbp:is_studied_for |
the behavior of curves on manifolds
|
| gptkbp:is_studied_in |
theoretical mathematics
|
| gptkbp:is_symmetric |
gptkb:true
|
| gptkbp:is_torsion-free |
gptkb:true
|
| gptkbp:is_used_in |
gptkb:general_relativity
|
| gptkbp:is_used_in_calculations_of |
geodesic equations
|
| gptkbp:is_used_in_the_formulation_of |
the geodesic deviation equation
|
| gptkbp:is_utilized_in |
numerical relativity
|
| gptkbp:is_utilized_in_the_study_of |
dynamical systems
|
| gptkbp:key_concept |
differential geometry
|
| gptkbp:key_feature |
the theory of relativity
|
| gptkbp:named_after |
gptkb:Tullio_Levi-Civita
|
| gptkbp:preserved_by |
inner product
|
| gptkbp:topics |
mathematical literature
|
| gptkbp:type_of |
affine connection
metric connection |
| gptkbp:was_involved_in |
Levi-Civita derivative
|
| gptkbp:bfsParent |
gptkb:Gregorio_Ricci-Curbastro
|
| gptkbp:bfsLayer |
7
|