Vanishing spinor projections in supergravity

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:
[itex]\Gamma_t \epsilon = \Gamma_r \epsilon = \Gamma_\theta \epsilon = \Gamma_\phi \epsilon = 0[/itex]
where [itex]\Gamma[/itex] is the Dirac gamma matrix, [itex]t[/itex] is time and [itex]r,\theta,\phi[/itex] are spherical coordinates on the 3-brane. [itex]\epsilon[/itex] 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.
 

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