> This idea was pointed out by mathematician Marcel Grossmann and published by Grossmann and Einstein in 1913.[7]
János Bolyai, not Bolshai. And certainly in the 1820s-1830s he investigated the Euclidean parallel postulate, arriving at a hyperbolic geometry in which it does not hold true (i.e., initially close parallel lines diverge), and eventually studying geometries which take no position on the parallel postulate. Lobachevsky also independently arrived at a hyperbolic geometry, and continued develop a substitute postulate for the parallel postulate.
However, all of the above is several long steps before developing differential geometry with its inner products encoding angles and distances on the tangent spaces at each point on an arbitrarily curved smooth manifold of higher dimensions, and an even longer one from the pseudo-Riemannian manifold of 3+1d General Relativity. Although many hands contributed to the positive inner product -> non-degenerate inner product, the reason anyone was doing that was because of Einstein's work on gravitation (in turn provoked in part by Poincaré's 1905 argument about Lorentz-invariance of the wave equation for gravitation, in the spirit of Special Relativity).