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According to the general theory of relativity, a massive body induces curvature in the surrounding spacetime. In this study, the surface curvature (SC) of neutron stars is computed using various curvature quantities derived from the relativistic mean-field, density-dependent RMF, and Skyrme-Hartree-Fock equations of states. Neutron star properties, including mass, radius, compactness, and central density, are calculated utilizing the Tolman-Oppenheimer-Volkoff equations. The analysis reveals a significant cubic correlation between the SC and compactness for the canonical 1.4 $M_{\odot}$ neutron star, with a correlation coefficient of 0.99, indicating an almost linear relationship. A similarly significant inverse cubic correlation is observed between the SC and the radius of the canonical star. However, these correlations diminish for the maximum mass NS. Furthermore, a universal relation between the SC and the dimensionless tidal deformability ($Λ$) for the canonical neutron star is established. Using the tidal deformability constraint of GW170817 ($Λ_{1.4} = 190_{-120}^{+390}$), the surface curvature is limited to SC$_{1.4} (10^{14}) = 2.87^{+0.30}_{-0.78}$ at a confidence level 90\%. Furthermore, the tidal deformability constraint of the secondary component in the GW190814 event ($Λ_{1.4} = 616_{-158}^{+273}$) offers a more stringent limit, with the result of SC$_{1.4} (10^{14}) = 2.03^{+0.27}_{-0.36}$. These findings indicate that the GW190814 event imposes more rigorous constraints on SC compared to GW170817.