We are working on concrete applications of the relativistic Schwarzschild model to the cosmos. In this report we relate the Gaussian curvature of space-time according to the Schwarzschild model with the gravitational redshift. The relativistic Schwarzschild model solves Einstein's equations exactly assuming a point gravitational mass and empty space in its vicinity. This model leads to a static and symmetric solution of the mathematical equation of space-time that allows its Gaussian curvature to be calculated at each point. We have calculated some curvature values and found an equation to calculate them which allows us to extend the results to a wider range of distances. We have quantitatively related this Gaussian curvature equation to the gravitational redshift equation by establishing a new equation between these two magnitudes. Finally, we carefully studied this found equation and applied it to the assumption of the supermassive black hole in our galaxy SAGITTARIUS A*.