53XX DIFFERENTIAL GEOMETRY (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
 5300 General reference works (handbooks, dictionaries, bibliographies, etc.)
 5301 Instructional exposition (textbooks, tutorial papers, etc.)
 5302 Research exposition (monographs, survey articles)
 5303 Historical (must also be assigned at least one classification number from Section 01)
 5304 Explicit machine computation and programs (not the theory of computation or programming)
 5306 Proceedings, conferences, collections, etc.
 53Axx Classical differential geometry

53Bxx Local differential geometry
(1)
 53Cxx Global differential geometry [See also 51H25, 58XX; for related bundle theory, see 55Rxx, 57Rxx]

53Dxx Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
(1)
 53Zxx Applications to physics