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< 53Bxx | 53-XX | 53Dxx >
53-XX Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx}
53Cxx Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]
53C05   Connections, general theory
53C07   Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]
53C08   Gerbes, differential characters: differential geometric aspects
53C10   $G$-structures
53C12   Foliations (differential geometric aspects) [See also 57R30, 57R32]
53C15   General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C17   Sub-Riemannian geometry
53C20   Global Riemannian geometry, including pinching [See also 31C12, 58B20]
53C21   Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
53C22   Geodesics [See also 58E10]
53C23   Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
53C24   Rigidity results
53C25   Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C26   Hyper-Kähler and quaternionic Kähler geometry, "special'' geometry
53C27   Spin and Spin${}^c$ geometry
53C28   Twistor methods [See also 32L25]
53C29   Issues of holonomy
53C30   Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
53C35   Symmetric spaces [See also 32M15, 57T15]
53C38   Calibrations and calibrated geometries
53C40   Global submanifolds [See also 53B25]
53C42   Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
53C43   Differential geometric aspects of harmonic maps [See also 58E20]
53C44   Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
53C45   Global surface theory (convex surfaces à la A. D. Aleksandrov)
53C50   Lorentz manifolds, manifolds with indefinite metrics
53C55   Hermitian and Kählerian manifolds [See also 32Cxx]
53C56   Other complex differential geometry [See also 32Cxx]
53C60   Finsler spaces and generalizations (areal metrics) [See also 58B20]
53C65   Integral geometry [See also 52A22, 60D05}; differential forms, currents, etc. \SeeMainly{58Axx]}
53C70   Direct methods ($G$-spaces of Busemann, etc.)
53C75   Geometric orders, order geometry [See also 51Lxx]
53C80   Applications to physics
53C99   None of the above, but in this section
< 53Bxx | 53-XX | 53Dxx >
 
 
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