I need to find the Killing vectors of a metric.
I initiate the session as
> with(DifferentialGeometry); with(Tensor); with(LieAlgebras);
> DGsetup([t, r, z, phi], M);
and enter my metric as
M > g1 := evalDG(-dt &t dt ...);
I do not have an unknown function in my metric but I have two free parameters (e.g. a and b).
M > K1 := KillingVectors(g1, parameters = [a, b]);
to find the Killing vectors (I also tried without giving the parameters). It finds some vectors but when I run
M > L1 := map(LieDerivative, K1, g1);
or for other members of K1, I cannot get zero but (a=a, b=b) case should give all zero.
I tried with some other metrics and got zero as it should be. I am sure that my metric is correct.
Is there any chance that Maple misses something, or better, am I missing something?