Mathematics Subject Classification 1991

53-XX Differential geometry, {For differential topology, See algebra and algebraic geometry), See also {06A08, 13F20, 13Hxx} ( 0 Dok.)

• 53-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 53-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 53-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 53-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 53-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 53-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 53Axx Classical differential geometry ( 0 Dok. )
• 53A04 Curves in Euclidean space ( 0 Dok.)
• 53A05 Surfaces in Euclidean space ( 0 Dok.)
• 53A07 Higher-dimension and -codimension surfaces in Euclidean $n$-space ( 0 Dok.)
• 53A10 Minimal surfaces, surfaces with prescribed mean curvature, See also {49Q05, 49Q10, 53C42} ( 0 Dok.)
• 53A15 Affine differential geometry ( 0 Dok.)
• 53A17 Kinematics ( 0 Dok.)
• 53A20 Projective differential geometry ( 0 Dok.)
• 53A25 Differential line geometry ( 0 Dok.)
• 53A30 Conformal differential geometry ( 0 Dok.)
• 53A35 Non-Euclidean differential geometry ( 0 Dok.)
• 53A40 Other special differential geometries ( 0 Dok.)
• 53A45 Vector and tensor analysis ( 0 Dok.)
• 53A50 Spinor analysis ( 0 Dok.)
• 53A55 Differential invariants (local theory), geometric objects ( 0 Dok.)
• 53A60 Geometry of webs, See also {14C21, 20N05} ( 0 Dok.)
• 53A99 None of the above but in this section ( 0 Dok.)
• 53Bxx Local differential geometry ( 0 Dok. )
• 53B05 Linear and affine connections ( 0 Dok.)
• 53B10 Projective connections ( 0 Dok.)
• 53B15 Other connections ( 0 Dok.)
• 53B20 Local Riemannian geometry ( 0 Dok.)
• 53B21 Methods of Riemannian geometry ( 0 Dok.)
• 53B25 Local submanifolds, See also {53C40} ( 0 Dok.)
• 53B30 Lorentz metrics, indefinite metrics ( 0 Dok.)
• 53B35 Hermitian and Kahlerian structures, See also {32Cxx} ( 0 Dok.)
• 53B40 Finsler spaces and generalizations (areal metrics) ( 0 Dok.)
• 53B50 Applications to physics ( 0 Dok.)
• 53B99 None of the above but in this section ( 0 Dok.)
• 53Cxx Global differential geometry, See also {51H25, 58-XX; for related bundle theory, See 55Rxx, 57Rxx} ( 0 Dok. )
• 53C05 Connections, general theory ( 0 Dok.)
• 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills), See also {32L07} ( 0 Dok.)
• 53C10 $G$-structures ( 0 Dok.)
• 53C12 Foliations (differential geometric aspects), See Also { 57R30, 57R32} ( 0 Dok.)
• 53C15 General geometric structures on manifolds (almost complex, contact, symplectic, almost product structures, etc.) ( 0 Dok.)
• 53C20 Global Riemannian geometry, including pinching, See Also { 31C12, 58B20} ( 0 Dok.)
• 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions, See also {58G30} ( 0 Dok.)
• 53C22 Geodesics, See also {58E10} ( 0 Dok.)
• 53C23 Global topological methods (a la Gromov) ( 0 Dok.)
• 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) ( 0 Dok.)
• 53C30 Homogeneous manifolds, See also {14M15, 14M17, 32M10, 57T15} ( 0 Dok.)
• 53C35 Symmetric spaces, See also {32M15, 57T15} ( 0 Dok.)
• 53C40 Global submanifolds, See also {53B25} ( 0 Dok.)
• 53C42 Immersions (minimal, prescribed curvature, tight, etc.), See also {49Q05, 49Q10, 53A10, 57R40, 57R42} ( 0 Dok.)
• 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov) ( 0 Dok.)
• 53C50 Lorentz manifolds, manifolds with indefinite metrics ( 0 Dok.)
• 53C55 Hermitian and Kahlerian manifolds, See also {32Cxx} ( 0 Dok.)
• 53C56 Other complex differential geometry, See also {32Cxx} ( 0 Dok.)
• 53C60 Finsler spaces and generalizations (areal metrics), See also {58B20} ( 0 Dok.)
• 53C65 Integral geometry, See also {52A22, 60D05}; differential forms, currents, etc. See mainly{58Axx} ( 0 Dok.)
• 53C70 Direct methods ($G$-spaces of Busemann, etc.) ( 0 Dok.)
• 53C75 Geometric orders, order geometry, See also {51Lxx} ( 0 Dok.)
• 53C80 Applications to physics ( 0 Dok.)
• 53C99 None of the above but in this section ( 0 Dok.)