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gptkbp:instanceOf
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branch of differential geometry
|
|
gptkbp:appliesTo
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gptkb:general_relativity
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|
gptkbp:concerns
|
smooth manifolds with Riemannian metric
|
|
gptkbp:developedBy
|
gptkb:Bernhard_Riemann
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|
https://www.w3.org/2000/01/rdf-schema#label
|
Riemannian Geometry
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|
gptkbp:introducedIn
|
19th century
|
|
gptkbp:namedAfter
|
gptkb:Bernhard_Riemann
|
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gptkbp:relatedTo
|
differential geometry
global analysis
metric geometry
|
|
gptkbp:studies
|
gptkb:music
gptkb:region
gptkb:Riemannian_manifolds
gptkb:spectral_geometry
gptkb:Riemann_curvature_tensor
gptkb:Gauss-Bonnet_theorem
gptkb:Hopf-Rinow_theorem
gptkb:Laplace-Beltrami_operator
gptkb:Myers'_theorem
gptkb:symmetric_spaces
gptkb:Bonnet-Myers_theorem
gptkb:Cartan-Hadamard_theorem
gptkb:Alexandrov_spaces
gptkb:Einstein_manifolds
gptkb:Gromov-Hausdorff_convergence
gptkb:Riemannian_covering_spaces
gptkb:Riemannian_foliations
gptkb:Riemannian_submersions
gptkb:Riemannian_symmetric_spaces
gptkb:harmonic_maps
geodesics
holonomy
minimal surfaces
Levi-Civita connection
Ricci curvature
curvature
isometries
parallel transport
scalar curvature
sectional curvature
comparison geometry
comparison theorems
Riemannian embeddings
Riemannian group actions
Riemannian immersions
Riemannian orbifolds
Riemannian submanifolds
manifolds of constant curvature
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gptkbp:uses
|
gptkb:Riemannian_manifold
|
|
gptkbp:bfsParent
|
gptkb:Manfredo_do_Carmo
gptkb:Graduate_Studies_in_Mathematics
|
|
gptkbp:bfsLayer
|
7
|