51 的分类
51-XX Geometry {For algebraic geometry, see 14-XX; for differential geometry, see 53-XX}
51Axx Linear incidence geometry
51A05 General theory of linear incidence geometry and projective geometries
51A10 Homomorphism, automorphism and dualities in linear incidence geometry
51A15 Linear incidence geometric structures with parallelism
51A20 Configuration theorems in linear incidence geometry
51A25 Algebraization in linear incidence geometry [See also 12Kxx, 20N05]
51A30 Desarguesian and Pappian geometries
51A35 Non-Desarguesian affine and projective planes
51A40 Translation planes and spreads in linear incidence geometry
51A45 Incidence structures embeddable into projective geometries
51A50 Polar geometry, symplectic spaces, orthogonal spaces
51A99 None of the above, but in this section
51Bxx Nonlinear incidence geometry
51B05 General theory of nonlinear incidence geometry
51B10 M¨obius geometries
51B15 Laguerre geometries
51B20 Minkowski geometries in nonlinear incidence geometry
51B25 Lie geometries in nonlinear incidence geometry
51B99 None of the above, but in this section
51Cxx Ring geometry (Hjelmslev, Barbilian, etc.)
51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
51C99 None of the above, but in this section
51Dxx Geometric closure systems
51D05 Abstract (Maeda) geometries
51D10 Abstract geometries with exchange axiom
51D15 Abstract geometries with parallelism
51D20 Combinatorial geometries and geometric closure systems [See also 05B25, 05B35]
51D25 Lattices of subspaces and geometric closure systems [See also 05B35]
51D30 Continuous geometries, geometric closure systems and related topics [See also 06Cxx]
51D99 None of the above, but in this section
51Exx Finite geometry and special incidence structures
51E05 General block designs in finite geometry [See also 05B05]
51E10 Steiner systems in finite geometry [See also 05B05]
51E12 Generalized quadrangles and generalized polygons in finite geometry
51E14 Finite partial geometries (general), nets, partial spreads
51E15 Finite affine and projective planes (geometric aspects)
51E20 Combinatorial structures in finite projective spaces [See also 05Bxx]
51E21 Blocking sets, ovals, k-arcs
51E22 Linear codes and caps in Galois spaces [See also 94B05]
51E23 Spreads and packing problems in finite geometry
51E24 Buildings and the geometry of diagrams
51E25 Other finite nonlinear geometries
51E26 Other finite linear geometries
51E30 Other finite incidence structures (geometric aspects) [See also 05B30]
51E99 None of the above, but in this section
51Fxx Metric geometry
51F05 Absolute planes in metric geometry
51F10 Absolute spaces in metric geometry
51F15 Reflection groups, reflection geometries [See also 20H10, 20H15] {For Coxeter groups, see 20F55}
51F20 Congruence and orthogonality in metric geometry [See also 20H05]
51F25 Orthogonal and unitary groups in metric geometry [See also 20H05]
51F30 Lipschitz and coarse geometry of metric spaces [See also 53C23]
51F99 None of the above, but in this section
51Gxx Ordered geometries (ordered incidence structures, etc.)
51G05 Ordered geometries (ordered incidence structures, etc.)
51G99 None of the above, but in this section
51Hxx Topological geometry
51H05 General theory of topological geometry
51H10 Topological linear incidence structures
51H15 Topological nonlinear incidence structures
51H20 Topological geometries on manifolds [See also 57-XX]
51H25 Geometries with differentiable structure [See also 53Cxx, especially 53C70]
51H30 Geometries with algebraic manifold structure [See also 14-XX]
51H99 None of the above, but in this section
51Jxx Incidence groups
51J05 General theory of incidence groups
51J10 Projective incidence groups
51J15 Kinematic spaces
51J20 Representation by near-fields and near-algebras [See also 12K05, 16Y30]
51J99 None of the above, but in this section
51Kxx Distance geometry
51K05 General theory of distance geometry
51K10 Synthetic differential geometry
51K99 None of the above, but in this section
51Lxx Geometric order structures [See also 53C75]
51L05 Geometry of orders of nondifferentiable curves
51L10 Directly differentiable curves in geometric order structures
51L15 n-vertex theorems via direct methods
51L20 Geometry of orders of surfaces
51L99 None of the above, but in this section
51Mxx Real and complex geometry
51M04 Elementary problems in Euclidean geometries
51M05 Euclidean geometries (general) and generalizations
51M09 Elementary problems in hyperbolic and elliptic geometries
51M10 Hyperbolic and elliptic geometries (general) and generalizations
51M15 Geometric constructions in real or complex geometry
51M16 Inequalities and extremum problems in real or complex geometry {For convex problems, see 52A40}
51M20 Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]
51M25 Length, area and volume in real or complex geometry [See also 26B15]
51M30 Line geometries and their generalizations [See also 53A25]
51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]
51M99 None of the above, but in this section
51Nxx Analytic and descriptive geometry
51N05 Descriptive geometry [See also 65D17, 68U07]
51N10 Affine analytic geometry
51N15 Projective analytic geometry
51N20 Euclidean analytic geometry
51N25 Analytic geometry with other transformation groups
51N30 Geometry of classical groups [See also 14L35, 20Gxx]
51N35 Questions of classical algebraic geometry [See also 14Nxx]
51N99 None of the above, but in this section
51Pxx Classical or axiomatic geometry and physics [Should also be assigned at least one other classification number from Sections 70 through 86]
51P05 Classical or axiomatic geometry and physics [Should also be assigned at least one other classification number from Sections 70 through 86]
51P99 None of the above, but in this section
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