53C05  Connections, general theory


53C07  Special connections and metrics on vector bundles (HermiteEinsteinYangMills) [See also 32Q20]


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  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 topological methods (à la Gromov)


53C24  Rigidity results


53C25  Special Riemannian manifolds (Einstein, Sasakian, etc.)


53C26  HyperKähler 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)


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]


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

