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.’
    • ‘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.’
    • ‘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.’


Riemannian geometry