La géométrie métrique des variétés riemanniennes (variations sur la formule a 2 = b 2 + c 2 – 2 b c cos α). Berger, Marcel. Élie Cartan et les mathématiques. Une métrique semi-Riemannienne de l’indice 0 n’est qu’une métrique Rie- nentielle sur une variété Introduction à la Géométrie Riemannienne par l’étude des. qui avait organisé une conférence de géométrie sous-riemannienne `a . `a la dimension infinie le cadre de la géométrie sous-riemannienne.

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Riekannienne of relativity Galilean relativity Galilean transformation Special relativity Doubly special relativity. Two-dimensional Plane Area Polygon. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugural lecture ” Ueber die Hypothesen, welche der Geometrie zu Grunde liegen ” “On the Hypotheses on which Geometry is Based”.

Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dimensions. Principle of relativity Theory of relativity Frame of reference Inertial frame of reference Rest frame Center-of-momentum frame Equivalence principle Mass—energy equivalence Special relativity Doubly special relativity de Sitter invariant special relativity World line Riemannian geometry.

Riemannian geometry was first put forward in generality by Bernhard Riemann in the 19th century.

### Géométrie riemannienne – PDF Drive

This page was last edited on 30 Decemberat Altitude Tiemannienne Pythagorean theorem. Retrieved from ” https: Introduction History Mathematical formulation Tests.

Elliptic geometry is also sometimes called “Riemannian geometry”. Most of the results can be found in the classic monograph by Jeff Cheeger and D. Square Rectangle Rhombus Rhomboid. By using this site, you agree to the Terms of Use and Privacy Policy. From Wikipedia, the free encyclopedia. It enabled the formulation of Einstein ‘s general theory of relativitymade profound impact on group theory and representation theoryas well as analysisand spurred the development of algebraic and differential topology.

Dislocations and Disclinations produce torsions and curvature.

The choice is made depending on its importance and elegance of formulation. Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach’s principle.

## Variété pseudo-riemannienne

Point Line segment ray Length. Riemannian geometry is the branch of differential geometry that studies Riemannian manifoldssmooth manifolds with a Riemannian metrici. In all of the following theorems we assume some local behavior of the space usually formulated using curvature assumption to derive some information about the global structure of the space, including either some information on the topological type of the manifold or on the behavior of points at “sufficiently large” distances.

Riemannian geometry Bernhard Riemann.

## Géométrie riemannienne

Time dilation Mass—energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Ladder paradox Twin paradox. Views Read Edit View history. There exists a close analogy of differential geometry with the mathematical structure of defects in rirmannienne crystals.

Volume Cube cuboid Cylinder Pyramid Sphere. This gives, in particular, local notions of anglelength of curvessurface area and volume.

It deals with a broad range of geometries whose metric properties vary from point to point, including the standard types of Non-Euclidean geometry. Fundamental concepts Principle of relativity Theory of relativity Frame of reference Inertial frame of reference Rest frame Center-of-momentum frame Equivalence principle Mass—energy equivalence Special relativity Doubly special relativity de Sitter invariant special relativity World line Riemannian geometry.

Kaluza—Klein theory Quantum gravity Supergravity. This list is oriented to those who already know the basic definitions and want to know what these definitions are about. Any smooth manifold admits a Riemannian metricwhich often helps to solve problems of differential topology.

Black hole Event horizon Singularity Two-body problem Gravitational waves: In other projects Wikimedia Commons.