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We construct supersymmetric completions of various curvature squared terms infive dimensional supergravity with eight supercharges. Adopting the dilatonWeyl multiplet, we obtain the minimal off-shell supersymmetric Ricci scalarsquared as well as all vector multiplets coupled curvature squared invariants.Since the minimal off-shell supersymmetric Riemann tensor squared andGauss-Bonnet combination in the dilaton Weyl multiplet have been obtainedbefore, both the minimal off-shell and the vector multiplets coupled curvaturesquared invariants in the dilation Weyl multiplet are complete. We alsoconstructed an off-shell Ricci scalar squared invariant utilizing the standardWeyl multiplet. The supersymmetric Ricci scalar squared in the standard Weylmultiplet is coupled to n number of vector multiplets by construction, and itdeforms the very special geometry. We found that in the supersymmetric AdS_5vacuum, the very special geometry defined on the moduli space is modified in asimple way. Finally, we study the magnetic string and electric black holesolutions in the presence of supersymmetric Ricci scalar squared.

All Off-Shell R^2 Invariants in Five Dimensional N=2 Supergravity