We use molecular dynamics simulations of particles interacting through a truncated Lennard-Jones potential to study the surface properties of the curved liquid-vapor interface. We determine the Tolman length delta, investigate its critical behavior, and provide first results for the rigidity constants of bending, k, and of Gaussian curvature, (k) over bar. The rigidity constant of bending, determined at three different temperatures, is found to be positive and of the order of one-half k(B)T. The rigidity constant of Gaussian curvature, determined at a single temperature, is of the same order of magnitude.