Abstract
The vector fields associated with Ricci flow and Ricci solitons in Riemann manifold has been studied and the correspondence between these vector fields and symmetries of spacetime manifold of general relativity has been established. The relationships between the symmetries of Petrov type D and N pure radiation fields and Ricci solitons have been explored. The solitons corresponding to Schwarzschild solution and Reissner-Nordstrom spacetime have been obtained.
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