definition 13.142 Killing tensor

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6368 · p. 529

ground object -- no derivation owed

Rests on

depends_on definition 13.139 Killing vector ¶
- depends_on definition 13.120 Isometry ¶
  - depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
    - depends_on definition 13.48 Differentiable manifold ¶
      - depends_on definition 13.47 Differentiable structure ¶
    - depends_on definition 13.84 Tensor ¶
      - depends_on definition 13.83 Covector ¶
      - depends_on definition 13.81 Vector on a manifold ¶
- depends_on equation 13.267 eq:mfd-lie-def ¶
depends_on definition 13.149 Metric compatibility ¶
- depends_on definition 13.145 Affine connection ¶
  - depends_on definition 13.90 Mixed tensor ¶
    - depends_on definition 13.89 Contravariant and covariant tensors ¶
      - depends_on definition 13.88 General coordinate transformation ¶
    - depends_on definition 13.88 General coordinate transformation ¶ ↺
  - depends_on definition 13.82 Vector field ¶
    - depends_on definition 13.81 Vector on a manifold ¶ ↺
- depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶ ↺
- depends_on definition 13.146 Parallel transport and autoparallels ¶
  - depends_on definition 13.145 Affine connection ¶ ↺
depends_on definition 13.91 Symmetric and antisymmetric parts ¶

Supports

depends_on example 13.144 The two Killing tensors every metric carries ¶
depends_on theorem 13.143 Killing tensors and geodesic invariants ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Killing vector	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6381
`depends_on`	→	Metric compatibility	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6381
`depends_on`	→	Symmetric and antisymmetric parts	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6381
`depends_on`	←	The two Killing tensors every metric carries	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6444
`depends_on`	←	Killing tensors and geodesic invariants	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6395