On Curved Manifolds and Deformed Spaces
Résumé
Riemannian geometry is the geometry of bent manifolds. However, as this paper shows in a tangible rather than formal way, it is also the geometry of deformed zones of space. Applying Riemannian geometry to zones of space enables us to understand General Relativity (GR) almost intuitively, and inspires our imagination. Space in GR is considered a continuous manifold, curved by energy/momentum. Both Einstein (1933) [1] and Feynman (1963) [2], however, considered the option of space being a deformed continuum rather than a bent continuous manifold. In the GDM (2017) [3], though, space is a 3D deformed lattice rather than a bent continuous manifold.
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