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)
A spacetime which as a pseudo-Riemannian manifold has (possibly) non-vanishing Riemann curvature is called curved. This corresponds to a non-trivial field of gravity.
A highly symmetric example of curved spacetime is the (anti-)de Sitter spacetime. Other important examples are black hole-spacetimes.
In contrast, a non-curved spacetime is called flat, the archetypical example being Minkowski spacetime.
Last revised on April 2, 2024 at 14:44:04. See the history of this page for a list of all contributions to it.