The Relativity of Geometry and Physical Space

What does the “relativity of geometry” mean? It means that the statement: a certain geometry holds for space is meaningless. There is not only one geometry but a plurality of non-Euclidean geometries (although the term refers to hyperbolic and elliptic geometry). What geometry will we apply to the physical space? There the geometry will return to its starting point of its empirical origin. Experiments will be carried out as in all sciences and the results of measurements will determine the geometry of the physical space.