In index notation, an operation named for this property is denoted with parentheses around the indices of a tensor. For 10 points each:
[10e] Name this property possessed by tensors that are invariant under the pullback of a given diffeomorphism. Euclidean space has this property of remaining the same under reflections, rotations, and translations.
ANSWER: symmetry [accept word forms like symmetric; accept symmetrization]
[10h] These objects are defined as having a covariant derivative that vanishes when symmetrized. The set of all of these objects for Minkowski space generates the Lie (“lee”) algebra of the Poincaré (“pwan-cah-RAY”) group.
ANSWER: Killing vector fields [or Killing vectors; or Killing fields; accept Killing tensors]
[10m] Killing vector fields generate flows that preserve this quantity. This tensor assigns an inner product between any two vectors on a manifold, thereby defining a notion of distance.
ANSWER: metric tensor
<Jeremy Cummings, Physics>