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.)
  • 13
    53C17
    Sub-Riemannian geometry
  • 40
    53C20
    Global Riemannian geometry, including pinching [See also 31C12, 58B20]
  • 48
    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
  • 16
    53C40
    Global submanifolds [See also 53B25]
  • 20
    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]
  • 28
    53C44
    Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
  • 11
    53C45
    Global surface theory (convex surfaces à la A. D. Aleksandrov)
  • 22
    53C50
    Lorentz manifolds, manifolds with indefinite metrics
  • 24
    53C55
    Hermitian and Kählerian manifolds [See also 32Cxx]
  • 1
    53C56
    Other complex differential geometry [See also 32Cxx]
  • 18
    53C60
    Finsler spaces and generalizations (areal metrics) [See also 58B20]
  • 22
    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

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