We study the fuzzy hyperboloids AdS^2 and dS^2 as brane solutions in matrix
models. The unitary representations of SO(2,1) required for quantum field
theory are identified, and explicit formulae for their realization in terms of
fuzzy wavefunctions are given. In a second part, we study the (A)dS^2 brane
geometry and its dynamics, as governed by a suitable matrix model. In
particular, we show that trace of the energy-momentum tensor of matter induces
transversal perturbations of the brane and of the Ricci scalar. This leads to a
linearized form of Henneaux-Teitelboim-type gravity, illustrating the mechanism
of emergent gravity in matrix models.Comment: 25 page