Study of the decay B0(B- 0)-->rho+rho-, and constraints on the Cabibbo-Kobayashi-Maskawa angle alpha.

Using a data sample of 89 x 10(6) Upsilon(4S)-->BB decays collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC, we measure the B0(B (0))-->rho(+)rho(-) branching fraction as [30+/-4(stat)+/-5(syst)]x10(-6) and a longitudinal polarization fraction of f(L)=0.99+/-0.03(stat)+0.04-0.03(syst). We measure the time-dependent-asymmetry parameters of the longitudinally polarized component of this decay as C(L)=-0.17+/-0.27(stat)+/-0.14(syst) and S(L)=-0.42+/-0.42(stat)+/-0.14(syst). We exclude values of alpha between 19 degrees and 71 degrees (90% C.L.).