Killing superalgebras for lorentzian five-manifolds

We calculate the relevant Spencer cohomology of minimal Poincar\'e superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on spinor bundle 5-dimensional lorentzian spin manifold. give definition bosonic backgrounds terms this data. By imposing constraints curvature connection, we recover field equations (ungauged) supergravity, but also find set for an $\mathfrak{sp}(1)$-valued one-form which interpret as data class rigid supersymmetric theories curved backgrounds. show that their existence is implied by equations. The maximally are characterised superalgebras explicitly described filtered deformations superalgebra.