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In mathematics, a space form is a complete Riemannian manifold M of constant sectional curvature K. The three most fundamental examples are Euclidean n -space, the n -dimensional sphere, and hyperbolic space, although a space form need not be simply connected .
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Jan 18, 2024 · A space $ M ^ {n} $ is called a spherical space form if $ M ^ {n} = S ^ {n} / \Gamma $, a Euclidean space form if $ M ^ {n} = E ^ {n} / \Gamma $ and a hyperbolic space form if $ M ^ {n} = \Lambda ^ {n} / \Gamma $; the fundamental group of $ M ^ {n} $ is isomorphic to $ \Gamma $.
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Space forms, that is two-dimensional or three-dimensional Riemannian manifolds (later on they were generalized to n dimensions) which are locally isometric to the space of a classical geometry, were an important theme in early algebraic (or geometric) topology.
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