53XX 


Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} 

53Bxx 

Local differential geometry 


53B05 
Linear and affine connections 


53B10 
Projective connections 


53B15 
Other connections 


53B20 
Local Riemannian geometry 


53B21 
Methods of Riemannian geometry 


53B25 
Local submanifolds [See also 53C40] 


53B30 
Lorentz metrics, indefinite metrics 


53B35 
Hermitian and Kählerian structures [See also 32Cxx] 


53B40 
Finsler spaces and generalizations (areal metrics) 


53B50 
Applications to physics 


53B99 
None of the above, but in this section 