Abstract
It is shown that under the condition ϕju k = ϕ k uj imposed on the mapping function the geodesics in conformai gravitational fields are the same. The following fact is also established: all conformally flat spaces satisfying this condition correspond to the gravitational fields of an ideal fluid.
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T. Y. Thomas, The Differential Invariants of Generalized Spaces, Cambridge (1934).
A. Z. Petrov, New Methods in the General Theory of Relativity [in Russian], Moscow (1966).
P. K. Rashevskii, Riemannian Geometry and Tensor Analysis [in Russian], Moscow (1967).
E. Kamke, Ordinary Differential Equations [Russian translation], Moscow (1961).
H. P. Robertson, Rev. Mod. Phys.,5, 62 (1933).
A. Friedmann, Zeits. f. Phys.,10, 377 (1922).
V. S. Brezhnev, Reports of the First Soviet Gravitational Conference [in Russian], Moscow State Univ. (1961).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 16–19, 1972.
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Obozov, V.I. On the projectivity of conformally flat spaces created by a hydrodynamical energy-momentum tensor. Soviet Physics Journal 15, 1395–1398 (1972). https://doi.org/10.1007/BF00892081
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DOI: https://doi.org/10.1007/BF00892081