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Mathematical Sciences Classification System

53Cxx - Global differential geometry
[See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]

• 20
  53C05
  Connections, general theory
• 9
  53C07
  Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]
• 1
  53C08
  Gerbes, differential characters: differential geometric aspects
• 8
  53C10
  $G$-structures
• 16
  53C12
  Foliations (differential geometric aspects) [See also 57R30, 57R32]
• 8
  53C15
  General geometric structures on manifolds (almost complex, almost product structures, etc.)
• 14
  53C17
  Sub-Riemannian geometry
• 40
  53C20
  Global Riemannian geometry, including pinching [See also 31C12, 58B20]
• 49
  53C21
  Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
• 10
  53C22
  Geodesics [See also 58E10]
• 14
  53C23
  Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
• 2
  53C24
  Rigidity results
• 18
  53C25
  Special Riemannian manifolds (Einstein, Sasakian, etc.)
• 6
  53C26
  Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
• 10
  53C27
  Spin and Spin${}^c$ geometry
• 3
  53C28
  Twistor methods [See also 32L25]
• 5
  53C29
  Issues of holonomy
• 6
  53C30
  Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
• 19
  53C35
  Symmetric spaces [See also 32M15, 57T15]
• 2
  53C38
  Calibrations and calibrated geometries
• 17
  53C40
  Global submanifolds [See also 53B25]
• 21
  53C42
  Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
• 14
  53C43
  Differential geometric aspects of harmonic maps [See also 58E20]
• 30
  53C44
  Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
• 11
  53C45
  Global surface theory (convex surfaces à la A. D. Aleksandrov)
• 23
  53C50
  Lorentz manifolds, manifolds with indefinite metrics
• 25
  53C55
  Hermitian and Kählerian manifolds [See also 32Cxx]
• 1
  53C56
  Other complex differential geometry [See also 32Cxx]
• 19
  53C60
  Finsler spaces and generalizations (areal metrics) [See also 58B20]
• 23
  53C65
  Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]
• 2
  53C70
  Direct methods ($G$-spaces of Busemann, etc.)
• 53C75
  Geometric orders, order geometry [See also 51Lxx]
• 14
  53C80
  Applications to physics
• 53C99
  None of the above, but in this section