Mathematics Subject Classification 1991

51-XX Geometry, {For algebraic geometry, See 14-XX} ( 0 Dok.)

• 51-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 51-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 51-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 51-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 51-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 51-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 51Axx Linear incidence geometry ( 0 Dok. )
• 51A05 General theory and projective geometries ( 0 Dok.)
• 51A10 Homomorphism, automorphism and dualities ( 0 Dok.)
• 51A15 Structures with parallelism ( 0 Dok.)
• 51A20 Configuration theorems ( 0 Dok.)
• 51A25 Algebraization, See also {12Kxx, 20N05} ( 0 Dok.)
• 51A30 Desarguesian and Pappian geometries ( 0 Dok.)
• 51A35 Non-Desarguesian affine and projective planes ( 0 Dok.)
• 51A40 Translation planes and spreads ( 0 Dok.)
• 51A45 Incidence structures imbeddable into projective geometries ( 0 Dok.)
• 51A50 Polar geometry, symplectic spaces, orthogonal spaces ( 0 Dok.)
• 51A99 None of the above but in this section ( 0 Dok.)
• 51Bxx Nonlinear incidence geometry ( 0 Dok. )
• 51B05 General theory ( 0 Dok.)
• 51B10 Mobius geometries ( 0 Dok.)
• 51B15 Laguerre geometries ( 0 Dok.)
• 51B20 Minkowski geometries ( 0 Dok.)
• 51B25 Lie geometries ( 0 Dok.)
• 51B99 None of the above but in this section ( 0 Dok.)
• 51C05 Ring geometry (Hjelmslev, Barbilian, etc.) ( 0 Dok.)
• 51Dxx Geometric closure systems ( 0 Dok. )
• 51D05 Abstract (Maeda) geometries ( 0 Dok.)
• 51D10 Abstract geometries with exchange axiom ( 0 Dok.)
• 51D15 Abstract geometries with parallelism ( 0 Dok.)
• 51D20 Combinatorial geometries, See also {05B25, 05B35} ( 0 Dok.)
• 51D25 Lattices of subspaces, See also {05B35} ( 0 Dok.)
• 51D30 Continuous geometries and related topics, See also {06Cxx} ( 0 Dok.)
• 51D99 None of the above but in this section ( 0 Dok.)
• 51Exx Finite geometry and special incidence structures ( 0 Dok. )
• 51E05 General block designs, See also {05B05} ( 0 Dok.)
• 51E10 Steiner systems ( 0 Dok.)
• 51E12 Generalized quadrangles, generalized polygons ( 0 Dok.)
• 51E14 Finite partial geometries (general), nets, partial spreads ( 0 Dok.)
• 51E15 Affine and projective planes ( 0 Dok.)
• 51E20 Combinatorial structures in finite projective spaces, See also {05Bxx} ( 0 Dok.)
• 51E21 Blocking sets, ovals, $k$-arcs ( 0 Dok.)
• 51E22 Linear codes and caps in Galois spaces, See also {94B05} ( 0 Dok.)
• 51E23 Spreads and packing problems ( 0 Dok.)
• 51E24 Buildings and the geometry of diagrams ( 0 Dok.)
• 51E25 Other finite nonlinear geometries ( 0 Dok.)
• 51E26 Other finite linear geometries ( 0 Dok.)
• 51E30 Other finite incidence structures, See also {05B30} ( 0 Dok.)
• 51E99 None of the above but in this section ( 0 Dok.)
• 51Fxx Metric geometry ( 0 Dok. )
• 51F05 Absolute planes ( 0 Dok.)
• 51F10 Absolute spaces ( 0 Dok.)
• 51F15 Reflection groups, reflection geometries, See also {20H10, 20H15; for Coxeter groups, See 20F55} ( 0 Dok.)
• 51F20 Congruence and orthogonality, See also {20H05} ( 0 Dok.)
• 51F25 Orthogonal and unitary groups, See also {20H05} ( 0 Dok.)
• 51F99 None of the above but in this section ( 0 Dok.)
• 51G05 Ordered geometries (ordered incidence structures, etc.) ( 0 Dok.)
• 51Hxx Topological geometry ( 0 Dok. )
• 51H05 General theory ( 0 Dok.)
• 51H10 Topological linear incidence structures ( 0 Dok.)
• 51H15 Topological nonlinear incidence structures ( 0 Dok.)
• 51H20 Topological geometries on manifolds, See also {57-XX} ( 0 Dok.)
• 51H25 Geometries with differentiable structure, See also {53Cxx, 53C70} ( 0 Dok.)
• 51H30 Geometries with algebraic manifold structure, See Also { 14-XX} ( 0 Dok.)
• 51H99 None of the above but in this section ( 0 Dok.)
• 51Jxx Incidence groups ( 0 Dok. )
• 51J05 General theory ( 0 Dok.)
• 51J10 Projective incidence groups ( 0 Dok.)
• 51J15 Kinematic spaces ( 0 Dok.)
• 51J20 Representation by near-fields and near-algebras, See Also {12K05, 16Y30} ( 0 Dok.)
• 51J99 None of the above but in this section ( 0 Dok.)
• 51Kxx Distance geometry ( 0 Dok. )
• 51K05 General theory ( 0 Dok.)
• 51K10 Synthetic differential geometry ( 0 Dok.)
• 51K99 None of the above but in this section ( 0 Dok.)
• 51Lxx Geometric order structures, See also {53C75} ( 0 Dok. )
• 51L05 Geometry of orders of nondifferentiable curves ( 0 Dok.)
• 51L10 Directly differentiable curves ( 0 Dok.)
• 51L15 $n$-vertex theorems via direct methods ( 0 Dok.)
• 51L20 Geometry of orders of surfaces ( 0 Dok.)
• 51L99 None of the above but in this section ( 0 Dok.)
• 51Mxx Real and complex geometry ( 0 Dok. )
• 51M04 Elementary problems in Euclidean geometries ( 0 Dok.)
• 51M05 Euclidean geometries (general) and generalizations ( 0 Dok.)
• 51M09 Elementary problems in hyperbolic and elliptic geometries ( 0 Dok.)
• 51M10 Hyperbolic and elliptic geometries (general) and generalizations ( 0 Dok.)
• 51M15 Geometric constructions ( 0 Dok.)
• 51M16 Inequalities and extremum problems, {For convex problems,See 52A40} ( 0 Dok.)
• 51M20 Polyhedra and polytopes; regular figures, division ofspaces, See also {51F15} ( 0 Dok.)
• 51M25 Length, area and volume, See also {26B15} ( 0 Dok.)
• 51M30 Line geometries and their generalizations, See also {53A25} ( 0 Dok.)
• 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and theirgeneralizations), See also {14M15} ( 0 Dok.)
• 51M99 None of the above but in this section ( 0 Dok.)
• 51Nxx Analytic and descriptive geometry ( 0 Dok. )
• 51N05 Descriptive geometry, See also {65D17, 68U07} ( 0 Dok.)
• 51N10 Affine analytic geometry ( 0 Dok.)
• 51N15 Projective analytic geometry ( 0 Dok.)
• 51N20 Euclidean analytic geometry ( 0 Dok.)
• 51N25 Analytic geometry with other transformation groups ( 0 Dok.)
• 51N30 Geometry of classical groups, See also {20Gxx, 14L35} ( 0 Dok.)
• 51N35 Questions of classical algebraic geometry, See also {14Nxx} ( 0 Dok.)
• 51N99 None of the above but in this section ( 0 Dok.)
• 51P05 Geometry and physics (should also be assigned at least one other classification number from Sections 70--86) ( 0 Dok.)