Abstract
When the expressions proposed by Einstein for the components of the energy-momentum tensor of matter in the state of a perfect fluid are substituted in the field equations of general relativity, these equations impose conditions to be satisfied by the space-time continuum of a perfect fluid. It is the purpose of this paper to give a geometrical characterization of these continua; to determine the conditions that the world-lines of flow be geodesics; to show that there is a geometry of paths for the space of a perfect fluid for which the world-lines of flow and of light are paths and that it is possible to find a space in correspondence with the giyen space such that the world-lines of flow and of light of the latter are represented by geodesics of the former; to indicate the significance of the cosmological solutions of Einstein and de Sitter in the general theory; and to determine the radially symmetric continua of a static fluid for which the spaces have constant Riemannian curvature. 1. Einstein space of a perfect fluid. Consider a four-dimensional Riemann space with the fundamental quadratic form
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