53Cxx Global differential geometry

• 53C05 Connections, general theory
• 53C07 Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills), See also {32L07}
• 53C10 $G$-structures
• 53C12 Foliations (differential geometric aspects), See Also {57R30, 57R32}
• 53C15 General geometric structures on manifolds (almost complex, contact, symplectic, almost product structures, etc.)
• 53C20 Global Riemannian geometry, including pinching, See Also {31C12, 58B20}
• 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions, See also {58G30}
• 53C22 Geodesics, See also {58E10}
• 53C23 Global topological methods (a la Gromov)
• 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
• 53C30 Homogeneous manifolds, See also {14M15, 14M17, 32M10, 57T15}
• 53C35 Symmetric spaces, See also {32M15, 57T15}
• 53C40 Global submanifolds, See also {53B25}
• 53C42 Immersions (minimal, prescribed curvature, tight, etc.), See also {49Q05, 49Q10, 53A10, 57R40, 57R42}
• 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)
• 53C50 Lorentz manifolds, manifolds with indefinite metrics
• 53C55 Hermitian and Kahlerian manifolds, See also {32Cxx}
• 53C56 Other complex differential geometry, See also {32Cxx}
• 53C60 Finsler spaces and generalizations (areal metrics), See also {58B20}
• 53C65 Integral geometry, See also {52A22, 60D05}; differential forms, currents, etc. See mainly{58Axx}
• 53C70 Direct methods ($G$-spaces of Busemann, etc.)
• 53C75 Geometric orders, order geometry, See also {51Lxx}
• 53C80 Applications to physics
• 53C99 None of the above but in this section