pseudo-Riemannian space فضای ِ دروژ-ریمانی fazâ-ye doruž-Riemanni
*Fr.: espace pseudo-riemannien*
A space with an affine connection (without torsion), at each point of which the tangent
space is a → *pseudo-Euclidean space*
(Encyclopedia of Mathematics, Kluwer Academic Publications,
Editor in chief I. M. Vinogradov, 1991). → *pseudo-*; → *Riemannian*;
→ *space*. |

Riemannian ریمانی Riemanni (#)
*Fr.: riemannien*
Of or pertaining to Georg Friedrich Bernhard Riemann (1826-1866) or his
mathematics findings.
→ * Riemannian geometry*,
→ * Riemannian manifold*,
→ * Riemannian metric*,
→ * Riemann problem*,
→ * Riemann curvature tensor*. After the German mathematician Georg Friedrich Bernhard Riemann (1826-1866), the inventor of
the elliptic form of → *non-Euclidean geometry*, who made important
contributions to analysis and differential geometry, some of them paving the way for
the later development of → *general relativity*. |

Riemannian geometry هندسهی ِ ریمانی hendese-ye Riemanni
*Fr.: géométrie riemannienne*
A → *non-Euclidean geometry* in which there are no
→ *parallel* lines, and the sum of the → *angle*s
of a → *triangle* is always greater than 180°.
Riemannian figures can be thought of as figures
constructed on a curved surface. The geometry is called *elliptic* because the section
formed by a plane that cuts the curved surface is an ellipse. → *Riemannian*; → *geometry*. |

Riemannian manifold بسلای ِ ریمانی baslâ-ye Riemanni
*Fr.: variété riemannienne*
A → *manifold* on which there is a defined
→ *Riemannian metric*
(Douglas N. Clark, 2000, Dictionary of Analysis, Calculus, and Differential Equations). → *Riemannian*; → *metric*. |

Riemannian metric متریک ِ ریمانی metrik-e Riemanni
*Fr.: métrique riemannienne*
A positive-definite inner product, (.,.)_{x}, on *T*_{x}(M),
the tangent space to a manifold *M* at *x*, for each
*x* ∈ *M*, which
varies continually with *x*
(Douglas N. Clark, Dictionary of Analysis, Calculus, and Differential Equations). → *Riemannian*; → *metric*. |