Abstract

 The paper treats geodesic mappings of quasi-Einstein spaces with gradient defining vector.
 
 Previously the authors defined three types of these spaces.
 In the present paper it is proved that there are no quasi-Einstein spaces of special type.
 It is demonstrated that quasi-Einstein spaces of main type are closed with respect to geodesic mappings.
 The spaces of particular type are proved to be geodesic $D$-symmetric spaces.
 
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