# A note on constant curvature solutions in cylindrically symmetric metric $fR$ Gravity - General Relativity and Quantum Cosmology

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Abstract: In the previous work we introduced a new static cylindrically symmetricvacuum solutions in Weyl coordinates in the context of the metric fR theoriesof gravity\cite{1}. Now we obtain a 2-parameter family of exact solutions whichcontains cosmological constant and a new parameter as $\beta$. This solutioncorresponds to a constant Ricci scalar. We proved that in $fR$ gravity, theconstant curvature solution in cylindrically symmetric cases is only one memberof the most generalized Tian family in GR. We show that our constant curvatureexact solution is applicable to the exterior of a string. Sensibility ofstability under initial conditions is discussed.