Manifold

History

The first to have conceived clearly of curves and surfaces as spaces by themselves was possibly Carl Friedrich Gauss, the founder of intrinsic differential geometry with his theorema egregium ('remarkable theorem'). Bernhard Riemann was the first to do extensive work that really required a generalization of manifolds to higher dimensions. Abelian varieties were at that time already implicitly known, as complex manifolds. Lagrangian mechanics and Hamiltonian mechanics, when considered geometrically, are also naturally manifold theories.

Related Topics:
Curve - Surface - Carl Friedrich Gauss - Differential geometry - Theorema egregium - Bernhard Riemann - Abelian varieties - Complex manifold - Lagrangian mechanics - Hamiltonian mechanics

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