53-XX |
|
|
Differential geometry {For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx} |
|
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 |
Differential geometric aspects of gerbes and differential characters |
|
|
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 |
|
|
53C18 |
Conformal structures on manifolds |
|
|
53C20 |
Global Riemannian geometry, including pinching [See also 31C12, 58B20] |
|
|
53C21 |
Methods of global Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] |
|
|
53C22 |
Geodesics in global differential geometry [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 Spin${}^c$ geometry |
|
|
53C28 |
Twistor methods in differential geometry [See also 32L25] |
|
|
53C29 |
Issues of holonomy in differential geometry |
|
|
53C30 |
Differential geometry of homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] |
|
|
53C35 |
Differential geometry of symmetric spaces [See also 32M15, 57T15] |
|
|
53C38 |
Calibrations and calibrated geometries |
|
|
53C40 |
Global submanifolds [See also 53B25] |
|
|
53C42 |
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] |
|
|
53C43 |
Differential geometric aspects of harmonic maps [See also 58E20] |
|
|
53C45 |
Global surface theory (convex surfaces à la A. D. Aleksandrov) |
|
|
53C50 |
Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
|
|
53C55 |
Global differential geometry of Hermitian and Kählerian manifolds [See also 32Qxx] |
|
|
53C56 |
Other complex differential geometry [See also 32Qxx] |
|
|
53C60 |
Global differential geometry of Finsler spaces and generalizations (areal metrics) [See also 58B20] |
|
|
53C65 |
Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx] |
|
|
53C70 |
Direct methods ($G$-spaces of Busemann, etc.) |
|
|
53C75 |
Geometric orders, order geometry [See also 51Lxx] |
|
|
53C80 |
Applications of global differential geometry to the sciences |
|
|
53C99 |
None of the above, but in this section |