  We calculate neutron star (NS) properties like mass $M$, radius $R$,
compactness $C$ and surface curvature (SC) using relativistic mean-field (RMF)
and Skyrme-Hartree-Fock (SHF) models. Predictive competence of the various RMF
and SHF parameter sets are discussed and compared with the NICER and pulsar
observational data. We try to correlate between some properties of the NS like
$C$, $R$ and SC. To calculate the correlations coefficient, we employ the
Pearson formula. We substantiate a correlation between the SC and $C$ for
canonical NS, and it shows a strong correlation with a coefficient of 0.992.
Similarly, we find another correlation between the radius and SC with a
coefficient of 0.982 for the canonical star. The three-dimensional correlations
are studied for the $C$, $R$ and SC with varying the masses of the NS. To
visualise the correlation between these quantities as mentioned above, both for
maximum and canonical mass, a $7\times7$ heat map is constructed, which gives
the correlations between each pair of quantities. We find that there is a
strong correlation between these pairs SC$_{1.4}$--$R_{1.4}$,
SC$_{1.4}$--$C_{1.4}$. The correlations become weaker for the maximum mass NS.
To find the correlation between the same quantities but for different masses of
the NS, we calculated the correlations coefficients for 1.5-1.8 $M_\odot$ NS.
There are also we get strong correlations between $C$, $R$ and SC.
