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We propose a model-independent way to determine the cosmic curvature usingthe Hubble parameter $H(z)$ measured with cosmic chronometers and the comovingdistance $D(z)$ inferred from HII galaxies. We employ Gaussian processes tosmooth the measure of distance and match it to $30$ values of $H(z)$. Thecurvature parameter $\Omega_k$ may be obtained individually for each such pair.The weighted average for the complete sample is $\Omega_k=-0.0013\pm0.0004$,suggesting a bias towards negative values. The accuracy of the curvaturemeasurement improves with increased redshift, however, given possiblesystematic effects associated with local inhomogeneities. We therefore alsoanalyze a high-redshift ($z>1.5$) sub-sample on its own, which is more likelyto reflect the geometry of the Universe on large, smooth scales. We find forthis set of data that $\Omega_k=-0.0111\pm0.0416$, consistent with zero tobetter than $1\sigma$. This result is in agreement with the spatially flatuniverse inferred from the cosmic microwave background observations. We expectthis method to yield even tighter constraints on the curvature parameter withfuture, more accurate observations of HII galaxies at high $z$.

A Model-Independent Measurement of the Spatial Curvature using Cosmic Chronometers and the HII Hubble Diagram