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  • 53-XX Differential geometry
  • 53Cxx Global differential geometry
  • 53C55 Hermitian and Kählerian manifolds

53Cxx Global differential geometry

  • 53C05 Connections, general theory
  • 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
  • 53C08 Gerbes, differential characters: differential geometric aspects
  • 53C10 G -structures
  • 53C12 Foliations (differential geometric aspects)
  • 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
  • 53C17 Sub-Riemannian geometry
  • 53C20 Global Riemannian geometry, including pinching
  • 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions
  • 53C22 Geodesics
  • 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 Spin c geometry
  • 53C28 Twistor methods
  • 53C29 Issues of holonomy
  • 53C30 Homogeneous manifolds
  • 53C35 Symmetric spaces
  • 53C38 Calibrations and calibrated geometries
  • 53C40 Global submanifolds
  • 53C42 Immersions (minimal, prescribed curvature, tight, etc.)
  • 53C43 Differential geometric aspects of harmonic maps
  • 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
  • 53C56 Other complex differential geometry
  • 53C60 Finsler spaces and generalizations (areal metrics)
  • 53C65 Integral geometry ; differential forms, currents, etc.
  • 53C70 Direct methods ( G -spaces of Busemann, etc.)
  • 53C75 Geometric orders, order geometry
  • 53C80 Applications to physics
  • 53C99 None of the above, but in this section
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