Riemannian geometry and manifolds
Geometría riemanniana y variedades
- Date
- 1854 · confidence high
- Place
- Göttingen, Germany
- Credited to
- Bernhard Riemann (habilitation lecture On the Hypotheses which lie at the Foundations of Geometry)
- People
- 👤 Bernhard Riemann1826–1866
- Field
- Knowledge & symbols
What was discovered
A generalisation of geometry to spaces of any dimension with a metric that varies from point to point, with the curvature tensor as an intrinsic measure. It provided the language of general relativity.
The lecture was delivered before Gauss in 1854 and published in 1868, after Riemann's death.
What it led to
- general relativity
- the tensor calculus of Ricci and Levi-Civita
- differential topology
- Thurston's geometrisation and Perelman's proof
Built on
- Non-Euclidean (hyperbolic) geometry1829-1832
- Gauss's Theorema Egregium
Made possible
- Riemann curvature tensor1861
- Global Positioning System (GPS)1978-1995
- Proof of the Poincaré and geometrization conjectures2002-2003
- GPS (relativistic corrections)
- cosmology