fundamental concepts in differential geometry
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
0.1 Manifolds
- •
manifold
- •
smooth manifold
- •
manifold with boundary
- •
boundary manifold
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Riemannian manifold
- •
chart
- •
coordinate function
- •
coordinate map
- •
coordinate neighborhood
- •
coordinate system
- •
submanifold
- •
immersion
- •
differential structure
- •
diffeomorphism
0.2 Vector and Tensor Fields
- •
vector field
- •
tensor product
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contraction
- •
exterior product
- •
differential form
- •
exterior derivative
- •
tensor field
- •
jet
- •
spinor field
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Lie bracket
- •
Lie derivative
- •
flow
- •
integrable
- •
Pfaffian system
- •
frame fields
- •
Lie groups and algebras
- •
fields as section
on bundles
0.3 Bundles and Connections
- •
fibre bundle
- •
vector bundle
- •
tangent bundle
- •
cotangent bundle
- •
jet bundle
- •
connection
- •
affine connection
- •
Riemannian metric
- •
curvature
- •
torsion
- •
geodesic
- •
homotopic
- •
space of connections
0.4 Gauge theory
- •
non-Abelian