Cartan magic formula L_X = i_X d + d i_X on differential forms; measures change along flow of vector field X; commutes with d and pulls-back; Killing equation L_X g = 0 defines isometry.
Cartan magic formula L_X = i_X d + d i_X on differential forms; measures change along flow of vector field X; commutes with d and pulls-back; Killing equation L_X g = 0 defines isometry.