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in this paper we: defined Riemannian spaces, conformal mappings, Einstein spaces, Riemannian symmetric spaces, Ricci spaces and Ricci symmetric spaces, recall the fundamental properties of these spaces
in this paper we: 1) defined Riemannian space , conformal mapping, Einstein space , Ricci recurrent Einstein space. 2) study conformal mapping between Einstein spaces corresponding flat surface, and Ricci recurrent Einstein space.
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