53Cxx Global differential geometry [See also 51H25, 58XX; for related bundle theory, see 55Rxx, 57Rxx]
 53C05 Connections, general theory
 53C07 Special connections and metrics on vector bundles (HermiteEinstein YangMills) [See also 32Q20]
 53C08 Gerbes, differential characters: differential geometric aspects
 53C10 Gstructures
 53C12 Foliations (differential geometric aspects) [See also 57R30, 57R32]
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
 53C17 SubRiemannian 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 HyperKähler and quaternionic Kähler geometry, \special" geometry
 53C27 Spin and Spinc 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 curvatureGeometric 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. [See mainly 58Axx]
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 53C70 Direct methods (Gspaces of Busemann, etc.)
 53C75 Geometric orders, order geometry [See also 51Lxx]
 53C80 Applications to physics
 53C99 None of the above, but in this section