Definition of Riemannian geometry in English:
A form of differential non-Euclidean geometry developed by Bernhard Riemann, used to describe curved space. It provided Einstein with a mathematical basis for his general theory of relativity.
- His interests had turned away from affine and projective differential geometry and turned towards Riemannian geometry.
- The argument relegating Euclidean and hyperbolic geometry to footnotes of Riemannian geometry would be valid only if one were conceiving them as the ‘standard’ geometries over the real numbers.
- His research on the theory of real algebraic varieties, Riemannian geometry, parabolic and elliptic equations was, however, extremely deep and significant in the development of all these topics.
Definition of Riemannian geometry in:
- US English dictionary