Vanishing spinor projections in supergravity

1. Feb 12, 2013

Professor_E

Hello all
I am working on a model in D=5 N=2 supergravity where the metric background is described by a time-dependent three brane, with one extra spatial dimension (a brane-world with bulk sort of set up). The vanishing of fermionic variations gives me the following weird projections:
$\Gamma_t \epsilon = \Gamma_r \epsilon = \Gamma_\theta \epsilon = \Gamma_\phi \epsilon = 0$
where $\Gamma$ is the Dirac gamma matrix, $t$ is time and $r,\theta,\phi$ are spherical coordinates on the 3-brane. $\epsilon$ is the N=2 SUSY spinor.
My question is: What is the physical meaning of these vanishing projections? Any reference that addresses this and similar issues that anyone can recommend?
Thanks.