Recovery of time-dependent coefficient on Riemannian manifold for hyperbolic equations

International audienceGiven (M, g), a compact connected Riemannian manifold of dimension d 2, with boundary ∂M , we study the inverse boundary value problem of determining a time-dependent potential q, appearing in the wave equation ∂ 2 t u−∆gu+q(t, x)u = 0 in M = (0, T)×M with T > 0. Under suitable geometric assumptions we prove global unique determination of q ∈ L ∞ (M) given the Cauchy data set on the whole boundary ∂M , or on certain subsets of ∂M. Our problem can be seen as an analogue of the Calderón problem on the Lorentzian manifold (M , dt 2 − g)