An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

   Homepage   
   


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Number of Results: 5 Search : Riemannian
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 → 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 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 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.