Mathematical Sciences Classification System
53Cxx - Global differential geometry
[See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]
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53C05Connections, general theory
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53C07Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]
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53C08Gerbes, differential characters: differential geometric aspects
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53C10$G$-structures
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53C12
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53C15General geometric structures on manifolds (almost complex, almost product structures, etc.)
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53C17Sub-Riemannian geometry
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53C20
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53C21Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
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53C22Geodesics [See also 58E10]
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53C23Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
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53C24Rigidity results
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53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)
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53C26Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
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53C27Spin and Spin${}^c$ geometry
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53C28Twistor methods [See also 32L25]
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53C29Issues of holonomy
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53C30
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53C35
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53C38Calibrations and calibrated geometries
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53C40Global submanifolds [See also 53B25]
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53C42
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53C43Differential geometric aspects of harmonic maps [See also 58E20]
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53C44Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
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53C45Global surface theory (convex surfaces à la A. D. Aleksandrov)
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53C50Lorentz manifolds, manifolds with indefinite metrics
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53C55Hermitian and Kählerian manifolds [See also 32Cxx]
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53C56Other complex differential geometry [See also 32Cxx]
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53C60Finsler spaces and generalizations (areal metrics) [See also 58B20]
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53C65
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53C70Direct methods ($G$-spaces of Busemann, etc.)
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53C75Geometric orders, order geometry [See also 51Lxx]
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53C80Applications to physics
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53C99None of the above, but in this section