53-XX Differential geometry {For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx} 134961
53Cxx Global differential geometry [See also 51H25, 58-XX] {For related bundle theory, see 55Rxx, 57Rxx} 80026
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) [See also 32Q20] 2110
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 9890
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 5736
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 2210
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 8114
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics) [See also 58B20] 3132
53C65 Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx] 2437