synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
manifolds and cobordisms
cobordism theory, Introduction
Definitions
Genera and invariants
Classification
Theorems
Riemannian geometry (sub-Riemannian geometry)
Like a Riemannian manifold is a smooth manifold equipped with a Riemannian metric, a pseudo-Riemannian manifold is a manifold equipped with a pseudo-Riemannian metric. Lorentzian manifolds, as well as Riemannian manifolds themselves, are special cases of pseudo-Riemannian manifolds.
Barrett O'Neill, Semi-Riemannian Geometry With Applications to Relativity, Pure and Applied Mathematics 103, Academic Press (1983) [ISBN:9780125267403]
Shlomo Sternberg, Semi-Riemannian Geometry and General Relativity (2003) [pdf, ark:/13960/t5m927d2v]
Shlomo Sternberg, Curvature in Mathematical Physics, Dover (2012) [ISBN:9780486478555]
Last revised on June 6, 2024 at 09:09:07. See the history of this page for a list of all contributions to it.