53XX 


Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} 

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 (HermiteEinsteinYangMills) [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 
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 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 