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 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 (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
