Abstract
Riemannian geometry is the geometry of bent manifolds. However, as this paper shows, it is also the geometry of deformed spaces. General Relativity (GR), based on Riemannian geometry, relates to space around the Sun and other masses as a bent 3D manifold.  
 
 Although a bent 3D space manifold in a 4D hyper-space is unimaginable, physicists accept this constraint. Our geometry of deformed spaces removes this constraint and shows that the Sun and other masses simply contract the 3D space around them. Thus, we are able to understand General Relativity (GR) almost intuitively - an intuition that inspires our imagination.
 
 Space in GR is considered a continuous manifold, bent (curved) by energy/momentum. Both Einstein (1933) and Feynman (1963), considered the option of space being a deformed continuum rather than a bent (curved) continuous manifold. We, however, consider space to be a 3D deformed lattice rather than a bent continuous manifold. The geometry presented in this paper is the geometry of this kind of space.
Highlights
We relate to space not as a passive static arena for fields and particles but as an active elastic entity
Riemannian geometry is the geometry of bent manifolds
Einstein was led to General Relativity (GR) by arguments that were un-related to a possible elastic 3D space
Summary
We relate to space not as a passive static arena for fields and particles but as an active elastic entity. The mathematical objects of GR are n-dimensional manifolds in hyper-spaces with more dimensions than n These are not necessarily the physical objects that GR accounts for. In n-dimensional elastic deformed spaces, Euclidian geometry is not valid and we are compelled to use Riemannian geometry. All of its elementary cells are of the same size, and Euclidian geometry is valid. When the density is not uniform, i.e., cells are of different sizes, an internal observer discovers that Euclidian geometry is not valid. When this internal observer measures circles, they find an Excess Radius δr that differs from zero.
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