Observational constraints on the non-flat $\Lambda CDM$ model and a null
  test using the transition redshift
  A natural extension of the standard cosmological model are models that
include curvature as a free parameter. In this work we study in detail the
observational constraints on the non-flat $\Lambda CDM$ model using the two
main geometric tests: SNIa and Hubble parameter measurements. In general we
show that the observational constraints on the parameters of the $\Lambda CDM$
model strongly depend on the curvature parameter. In particular, we study the
constraints on the transition redshift ($z_{t}$) of a universe dominated by
matter for a universe dominated by the cosmological constant. Using this
observable we construct a new null test defining $\zeta = z_{t, flat}-z_{t, non
flat}$. This test depends only on the data of the Hubble parameter, the Hubble
constant and the matter density parameter. However, it does not depend on
derivative of an observable as generally many tests in the literature. To
reconstruct this test, we use the Gaussian process method. When we use the
best-fit parameters values of $PLANCK/2018$, we find no evidence of a
disagreement between the data and the standard model (flat $\Lambda CDM$), but
if we use the value $H_{0}$ from $RIESS/2018$ we found a disagreement with
respect at the standard model. However, it is important to note that the Hubble
parameter data has large errors for a solid statistical analysis.
