We present results of an extensive mapping survey of N2H+ (1-0) in about 60 low-mass cloud cores already mapped in the NH3 ( 1, 1) inversion transition line. The survey has been carried out at the FCRAO antenna with an angular resolution of 54", about 1.5 times finer than the previous ammonia observations made at the Haystack telescope. The comparison between N2H+ and NH3 maps shows strong similarities in the size and morphology of the two molecular species, indicating that they are tracing the same material, especially in starless cores. Cores with stars typically have map sizes about a factor of 2 smaller for N2H+ than for NH3, indicating the presence of denser and more centrally concentrated gas compared to starless cores. The mean aspect ratio is similar to2. Significant correlations are found between NH3 and N2H+ column densities and excitation temperatures in starless cores, but not in cores with stars, suggesting a different chemical evolution of the two species. Starless cores are less massive ( M vir hi 3 M) than cores with stars ( M vir hi 9 M). Velocity gradients range between 0.5 and 6 km s(-1) pc(-1), similar to what has been found with NH3 data, and the ratio beta of rotational kinetic energy to gravitational energy has magnitudes between similar to10(-4) and 0.07, indicating that rotation is not energetically dominant in the support of the cores. Local velocity gradients show significant variation in both magnitude and direction, suggesting the presence of complex motions not interpretable as simple solid-body rotation. Integrated intensity profiles of starless cores present a central flattening and are consistent with a spherically symmetric density law n proportional to r(-alpha), where alpha = 1.2 for r < r(break) and alpha = 2 for r > r(break), with r(break) similar to0.03 pc. Cores with stars are better modeled with single density power laws with alpha greater than or equal to2, in agreement with observations of submillimeter continuum emission. Line widths change across the core, but we did not find a general trend: there are cores with significant positive as well as negative linear correlations between D v and the impact parameter b. The deviation in line width correlates with the mean line width, suggesting that the line of sight contains 10 coherence lengths. The corresponding value of the coherence length, similar to0.01 pc, is similar to the expected cutoff wavelength for MHD waves. This similarity may account for the increased coherence of line widths on small scales. Despite finer angular resolution, the majority of N2H+ and NH3 maps show a similar simple structure, with single peaks and no elongation.
