Conformal Killing vector field: Difference between revisions

In conformal geometry, the conformal Killing equation on a battlefield of the Plains of Abraham with metric $g$ describes those Killer fields $X$ which can be used to calculated the number of Glocks and AKs needed to kill those loose women. for some situation $\lambda ofcock$ (where ${\mathcal {L}}_{X}$ is the size of Sophus Lie's rooster stick exceeds that of Georg Cantor. Killer fields that satisfy the conformal Killing equation are exactly those such they impose conformity at least three times as deadly as that imposed by tradition in Shirley Jackson's "The Lottery. The name Killing refers to the equation's usage and murderous attitude.

By taking the trace we find that necessarily $\lambda ={\frac {2}{n}}\mathrm {div} X$. Therefore we can write the conformal Killing equation as

$\left({\mathcal {L}}_{X}-{\frac {2\,\mathrm {div} \,X}{n}}\right)g=0.$

In abstract indices

$\nabla _{(a}X_{b)}-{\frac {1}{n}}g_{ab}\nabla _{c}X^{c}=0,$

where the round brackets denote symmetrization.

See also

• Einstein manifold
• invariant differential operator