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We prove that a connected complex space form ($M^n$,g,J) with n ≥ 4 can be characterized by the Ricci-semi-symmetry condition ${\tilde{R}}_{XY}·\tilde{\varrho }=0$ and by the semi-parallel condition ${\tilde{R}}_{XY}·\sigma =0$, considering special choices of tangent vectors $X,Y$ to small geodesic spheres or geodesic tubes (that is, tubes about geodesics), where $\tilde{R}$, $\tilde{\varrho }$ and $\sigma$ denote the Riemann curvature tensor, the corresponding Ricci tensor of type (0,2) and the second fundamental form of the spheres or tubes and where ${\tilde{R}}_{XY}$ acts as a derivation.