An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 5 Search : Riemannian
 pseudo-Riemannian space   فضای ِ دروژ-ریمانی   fazâ-ye doruž-RiemanniFr.: 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 RiemanniFr.: géométrie riemannienne   A → non-Euclidean geometry in which there are no → parallel lines, and the sum of the → angles 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 RiemanniFr.: 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 RiemanniFr.: métrique riemannienne   A positive-definite inner product, (.,.)x, on Tx(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.