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fundamental concepts in differential geometry
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The following is an index of fundamental concepts in differental geometry. It only deals with basic concepts which are common to all branches of differential geometry. For concepts pertinent to specific branches of differential geometry, please see concepts in symplectic geometry and concepts in Riemannian geometry
- manifold
- smooth manifold
- manifold with boundary
- boundary manifold
- Riemannian manifold
- chart
- coordinate function
- coordinate map
- coordinate neighborhood
- coordinate system
- submanifold
- immersion
- differential structure
- diffeomorphism
- vector field
- tensor product
- contraction
- exterior product
- differential form
- exterior derivative
- tensor field
- jet
- spinor field
- Lie bracket
- Lie derivative
- flow
- integrable
- Pfaffian system
- frame fields
- Lie groups and algebras
- fields as section on bundles
- fibre bundle
- vector bundle
- tangent bundle
- cotangent bundle
- jet bundle
- connection
- affine connection
- Riemannian metric
- curvature
- torsion
- geodesic
- homotopic classification and characteristic classes
- space of connections
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"fundamental concepts in differential geometry" is owned by rspuzio. [ full author list (4) ]
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Cross-references: theory, gauge, non-Abelian, classes, characteristic, homotopic, geodesic, torsion, curvature, Riemannian metric, affine connection, connection, jet bundle, cotangent bundle, tangent bundle, vector bundle, fibre bundle, section, algebras, Lie groups, frame, Pfaffian, flow, Lie derivative, Lie bracket, spinor, jet, field, tensor, exterior derivative, differential form, exterior product, contraction, tensor product, vector field, diffeomorphism, differential structure, immersion, submanifold, coordinate system, neighborhood, map, function, coordinate, chart, Riemannian manifold, boundary, manifold, concepts in symplectic geometry, differential geometry, branches, geometry, index
There is 1 reference to this entry.
This is version 12 of fundamental concepts in differential geometry, born on 2004-11-02, modified 2008-10-20.
Object id is 6441, canonical name is FundamentalConceptsInDifferentialGeometry.
Accessed 4537 times total.
Classification:
| AMS MSC: | 53-00 (Differential geometry :: General reference works ) |
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Pending Errata and Addenda
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