Based on the rigidly rotating progenitor models found to be able to grow up to the canonical Chandrasekhar mass limit and beyond, and undergo a thermonuclear explosion, we compute the explosions, detailed nucleosynthesis, and corresponding light curves by means of a one-dimensional hydrodynamic code. Our results show that the inclusion of rotation in the evolution of the progenitors determines, in a natural way, a variation in the explosive physical conditions, mainly different explosive ignition densities (2:08 ; 10 9 to 3:34 ; 10 9 g cm À3 ), total masses (1.39-1.48 M ), and binding energies (À5:3 ; 10 50 to À6:6 ; 10 50 ergs). Such a spread is related to the rotational velocity at the explosive carbon ignition stage and to the efficiency of angular momentum loss during the last part of the progenitor evolution. We explore the final outcome in the framework of the delayed detonation explosion models by fixing the value of the transition density and by considering two different braking efficiencies. Within the explored parameter space, the bolometric light curves at maximum show differences of $0.1 mag due to the different amount of 56 Ni synthesized during the explosion. Although rigid rotation cannot be considered responsible for the diversities in the observational properties of SNe Ia, it could explain the dispersion in the magnitude at maximum of standardized events. We also find that those models with high ignition densities produce a central remnant in which most of the neutron-rich species synthesized during the explosion are trapped.