Concept information
Terme préférentiel
Riemannian geometry
Définition
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Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riemannian_geometry)
Concept générique
Concepts spécifiques
- Abel-Jacobi map
- Beltrami's theorem
- Cartan-Alexandrov-Toponogov space
- Cartan-Hadamard theorem
- Cotton tensor
- Einstein tensor
- exponential map
- fundamental theorem of Riemannian geometry
- Gauss-Bonnet formula
- Gauss's lemma
- geodesic
- geodesic deviation
- Gromov-Hausdorff distance
- harmonic coordinates
- Hodge duality
- Hopf-Rinow theorem
- Killing spinor
- Laplace-Beltrami operator
- Levi-Civita connection
- Loewner's torus inequality
- Margulis lemma
- musical isomorphism
- Myers's theorem
- Nash embedding theorem
- parallel transport
- Ricci curvature tensor
- Riemannian manifold
- Riemannian metric
- Ruppeiner geometry
- soul theorem
- spectral geometry
- sphere theorem
- spinor bundle
- Synge's theorem
- Toponogov's theorem
- Weyl curvature tensor
Traductions
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français
URI
http://data.loterre.fr/ark:/67375/PSR-TTBXXW26-C
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