On Bent Manifolds and Deformed Spaces | Barak | Journal of Mathematics Research | CCSE

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