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In this work we perform a general study of properties of a class of locallysymmetric embedded hypersurfaces in spacetimes admitting a $1+1+2$ spacetimedecomposition. The hypersurfaces are given by specifying the form of the Riccitensor with respect to the induced metric. These are slices of constant time inthe spacetime. Firstly, the form of the Ricci tensor for general hypersurfacesis obtained and the conditions under which the general case reduces to those ofconstant time slices are specified. We provide a characterization of thesehypersurfaces, with key physical quantities in the spacetime playing a role inspecifying the local geometry of these hypersurfaces. Furthermore, weinvestigate the case where these hypersurfaces admit a Ricci soliton structure.The particular cases where the vector fields associated to the solitons areKilling or conformal Killing vector fields are analyzed. Finally, in thecontext of spacetimes with local rotational symmetry it is shown that, onlyspacetimes in this class with vanishing rotation and spatial twist can admitthe hypersurface types considered, and that the hypersurfaces are necessarilyflat. And if such hypersurface do admit a Ricci soliton structure, the solitonis steady, with the components of the soliton field being constants.

On some locally symmetric embedded spaces with non-negative scalar curvature and their characterization