Retrieving "Unit Ball Model" from the archives

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  1. Riemannian Manifold

    Linked via "unit ball model"

    | Euclidean Space ($\mathbb{R}^n$) | $K=0$ | $(n, 0)$ | Trivial Holonomy Group ($\text{SO}(n)$ or trivial) |
    | Sphere ($S^n$) | $K > 0$ (Constant) | $(n, 0)$ | Maximal symmetry group $\text{O}(n+1)$ |
    | Hyperbolic Space ($\mathbb{H}^n$) | $K < 0$ (Constant) | $(n, 0)$ | Derived from the unit ball model, exhibiting unusual "hyperbolic viscosity" |
    A particularly esoteric class involves manifolds where the components of the metric tensor a…