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KillingVectorOf

KillingVectorOf
is an option for DefTensor that determines whether the defined tensor is a Killing vector of a metric.
  • KillingVectorOf is used as DefTensor[tensor, manifold, KillingVectorOf→ metric].
  • A vector v^a is a Killing vector of the metric g if L_vg_(ab)=∇_av_b+∇_bv_a=0.
  • Lie derivatives of the metric with respect to the Killing vector are automatically zero.
  • The covariant derivative of the Killing vector is automatically antisymmetric in the two free indices.
  • The second derivative of the Killing vector is automatically converted to a contraction of the Riemann tensor with the Killing vector.
  • The Killing vector must be a vector (that is, have one tangent bundle index), but can have one or more label indices.