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A family of exact relativistic stellar models is described. The familygeneralizes Buchdahl's n=1 polytropic solution. The matter content is a perfectfluid and, excluding Buchdahl's original model, it behaves as a liquid at lowpressures in the sense that the energy density is non-zero in the zero pressurelimit. The equation of state has two free parameters, a scaling and a stiffnessparameter. Depending on the value of the stiffness parameter the fluidbehaviour can be divided in four different types. Physical quantities such asmasses, radii and surface redshifts as well as density and pressure profilesare calculated and displayed graphically. Leaving the details to a laterpublication, it is noted that one of the equation of state types can quiteaccurately approximate the equation of state of real cold matter in the outerregions of neutron stars. Finally, it is observed that the given equation ofstate does not admit models with a conical singularity at the center.Comment: 19 pages, 12 figures (16 eps files), LaTeX2e with the standard  packages amssymb, amsmath, graphicx, subfigure, psfra

Exact relativistic stellar models with liquid surface: I. Generalizing Buchdahl's n = 1 polytrope