| 53-XX | | Prev: 52 | Up: Top | Next: 54 | |
| Differential geometry | |
| {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} |
53-00
| General reference works (handbooks, dictionaries, bibliographies, etc.)
| 53-01
| Instructional exposition (textbooks, tutorial papers, etc.)
| 53-02
| Research exposition (monographs, survey articles)
| 53-03
| Historical (must also be assigned at least one classification number from Section 01)
| 53-04
| Explicit machine computation and programs (not the theory of computation or programming)
| 53-06
| Proceedings, conferences, collections, etc.
| |
53Axx
| Classical differential geometry
[xref: 46T05]
| 53A04 |
Curves in Euclidean space
[xref: 52A10]
| 53A05 |
Surfaces in Euclidean space
[xref: 52A15]
| 53A07 |
Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
[xref: 52A20]
| 53A10 |
Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
[xref: 49Q05, 53C42]
| 53A15 |
Affine differential geometry
| 53A17 |
Kinematics
[xref: 70Bxx]
| 53A20 |
Projective differential geometry
| 53A25 |
Differential line geometry
[xref: 51M30]
| 53A30 |
Conformal differential geometry
| 53A35 |
Non-Euclidean differential geometry
| 53A40 |
Other special differential geometries
| 53A45 |
Vector and tensor analysis
| 53A55 |
Differential invariants (local theory), geometric objects
| 53A60 |
Geometry of webs [See also 14C21, 20N05]
[xref: 14C21]
| 53A99 |
None of the above, but in this section
| |
53Bxx
| Local differential geometry
| 53B05 |
Linear and affine connections
| 53B10 |
Projective connections
| 53B15 |
Other connections
| 53B20 |
Local Riemannian geometry
| 53B21 |
Methods of Riemannian geometry
| 53B25 |
Local submanifolds [See also 53C40]
[xref: 53C40]
| 53B30 |
Lorentz metrics, indefinite metrics
| 53B35 |
Hermitian and Kählerian structures [See also 32Cxx]
| 53B40 |
Finsler spaces and generalizations (areal metrics)
| 53B50 |
Applications to physics
| 53B99 |
None of the above, but in this section
| |
53Cxx
| Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]
[xref: 32Q20, 51H25, 58Dxx, 58Jxx, 70G45]
| 53C05 |
Connections, general theory
| 53C07 |
Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]
[xref: 81T13]
| 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
| 53C20 |
Global Riemannian geometry, including pinching [See also 31C12, 58B20]
[xref: 31C12, 58B20]
| 53C21 |
Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
| 53C22 |
Geodesics [See also 58E10]
| 53C23 |
Global topological methods (à la Gromov)
| 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 [See also 32L25]
[xref: 32L25]
| 53C29 |
Issues of holonomy
| 53C30 |
Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
[xref: 14M17]
| 53C35 |
Symmetric spaces [See also 32M15, 57T15]
[xref: 32M15]
| 53C38 |
Calibrations and calibrated geometries
| 53C40 |
Global submanifolds [See also 53B25]
[xref: 53B25]
| 53C42 |
Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
[xref: 53A10]
| 53C43 |
Differential geometric aspects of harmonic maps [See also 58E20]
[xref: 58E20]
| 53C44 |
Geometric evolution equations (mean curvature flow)
| 53C45 |
Global surface theory (convex surfaces à la A. D. Aleksandrov)
[xref: 52A15, 52A20]
| 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]
[xref: 58B20]
| 53C65 |
Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc.] [See mainly 58Axx]
[xref: 52A22, 58A25, 60D05]
| 53C70 |
Direct methods ($G$-spaces of Busemann, etc.)
[xref: 51H25]
| 53C75 |
Geometric orders, order geometry [See also 51Lxx]
[xref: 51Lxx]
| 53C80 |
Applications to physics
| 53C99 |
None of the above, but in this section
| |
53Dxx
| Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
[xref: 37Jxx, 70G45]
| 53D05 |
Symplectic manifolds, general
| 53D10 |
Contact manifolds, general
[xref: 37J55]
| 53D12 |
Lagrangian submanifolds; Maslov index
| 53D15 |
Almost contact and almost symplectic manifolds
| 53D17 |
Poisson manifolds
| 53D20 |
Momentum maps; symplectic reduction
[xref: 37J15]
| 53D22 |
Canonical transformations
| 53D25 |
Geodesic flows
| 53D30 |
Symplectic structures of moduli spaces
| 53D35 |
Global theory of symplectic and contact manifolds [See also 57Rxx]
| 53D40 |
Floer homology and cohomology, symplectic aspects
| 53D45 |
Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
[xref: 14N35]
| 53D50 |
Geometric quantization
[xref: 81S10]
| 53D55 |
Deformation quantization, star products
| 53D99 |
None of the above, but in this section
| |
53Z05
| Applications to physics
| |