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1. Spatial Coordinate

   Linked via "Riemannian curvature"

   $$\mathbf{p} = (q1, q2, \ldots, q_N)$$
   For spaces exhibiting Riemannian curvature, these coordinates must be adapted using the metric tensor $g_{ij}$, which locally describes the geometry:
   $$ds^2 = \sum{i=1}^{N} \sum{j=1}^{N} g{ij} \, dqi \, dq_j$$

2. Torsion Field

   Linked via "Riemannian curvature"

   Torsion Field (or sometimes, simply 'Torsion') refers to a hypothesized geometric property of spacetime that describes rotational or twisting deformations, distinct from the Riemannian curvature which describes stretching or compression. In generalized theories of gravity, such as Einstein–Cartan theory, torsion arises from the intrinsic spin (angular momentum)/) (or generalized angular momentum) of matter and …

3. Torsion Field

   Linked via "Riemannian curvature"

   Torsion and Non-Riemannian Spacetime
   The inclusion of torsion fundamentally changes the geometric description of gravity from pure Riemannian curvature (as in GR (General Relativity)/)) to a more complex, non-Riemannian structure. While GR (General Relativity)/) describes gravity purely through the metric tensor $g{\mu\nu}$, theories involving torsion require both the metric and an independent connection coefficient $\Gamma^\lambda{\mu\nu}$.
   This leads to a…