Differential Geometry
Differentiable Manifold
Tangent Vector
Tangent Space
Exterior Derivative
k-form φ = g dxi = g dxi1 ∧ ⋯ ∧ dxik. dφ = Dxj g xj ∧ xi. General k-form ω = fi dxi. dφ = d
Covariant Derivative
Riemannian Geometry
Connection
Affine Connection
Levi-Civita Connection
Metric Connection
Symplectic Geometry
Tensor Density
Pseudo-Riemannian Manifold
Derivation
Differential Form
D
Laplace–Beltrami Operator
Hodge Theory
ω = dα + δβ + γ, Δλ = 0. Ωk
Complex Differential Form
Lie Group
Continuous Symmetry
Lie Derivative
References
- An Invitation to Synthetic Differential Geometry. Sergio Fabi. 2017.
- New Methods for Old Spaces: Synthetic Differential Geometry. Anders Kock. 2017.
- Synthetic Geometry of Manifolds. Anders Kock. 2010.
- Synthetic Differential Geometry: An application to Einstein’s Equivalence Principle. Tim de Laat. 2008.
- Synthetic Differential Geometry. Anders Kock. 2006.