Definition of Riemannian geometry in English:

Riemannian geometry


  • A form of differential non-Euclidean geometry developed by Riemann, used to describe curved space. It provided Einstein with a mathematical basis for his general theory of relativity.

    • ‘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.’
    • ‘His interests had turned away from affine and projective differential geometry and turned towards Riemannian geometry.’
    • ‘The second stage started after 1921 when Eisenhart, prompted by Einstein's general theory of relativity and the related geometries, studied generalisations of Riemannian geometry.’
    • ‘He gave a reducibility theorem for Riemann spaces which is fundamental in the development of 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.’


Riemannian geometry