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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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There exists a close analogy of differential geometry with the mathematical structure of defects in regular crystals. 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 Rriemannienne invariant special relativity World line Riemannian geometry.

Black hole Event horizon Singularity Two-body problem Gravitational waves: Kaluza—Klein theory Quantum gravity Supergravity.

What follows is an incomplete list of the most classical theorems in Riemannian geometry. Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach’s principle. This list is oriented to those who already know the basic riemanniehne and want to know what these definitions are about. Riemannian geometry Bernhard Riemann. This gives, in particular, local notions of anglelength of curvessurface area and volume. Introduction History Mathematical formulation Tests.

The formulations given are far from being very exact or the most general. Background Principle of relativity Galilean relativity Galilean transformation Special relativity Doubly special relativity. Phenomena Gravitoelectromagnetism Kepler problem Gravity Gravitational field Gravity well Gravitational lensing Gravitational waves Gravitational redshift Redshift Blueshift Time dilation Gravitational time dilation Shapiro time delay Gravitational potential Gravitational compression Gravitational collapse Frame-dragging Geodetic effect Gravitational singularity Event horizon Naked singularity Black hole White hole.

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Variété pseudo-riemannienne — Wikipédia

It is a very broad and abstract generalization of the differential geometry of surfaces in R 3. 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.

Background Introduction Mathematical formulation. 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.

From Wikipedia, the free encyclopedia. Any smooth manifold admits a Riemannian metricwhich often helps to solve problems of differential topology. Light cone World line Minkowski diagram Biquaternions Minkowski space.

Variété pseudo-riemannienne

Time dilation Mass—energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas geomwtrie Ladder paradox Twin paradox. Retrieved from ” https: The choice is made depending on its importance and elegance of formulation.

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 geometie the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dimensions.

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This page was last edited on 30 Decemberat It also serves as an entry level for the more complicated structure of pseudo-Riemannian manifoldswhich in four dimensions are the main objects of the theory of general relativity. Square Rectangle Rhombus Rhomboid. In other projects Wikimedia Commons. Elliptic geometry is also sometimes called “Riemannian geometry”. Other generalizations of Riemannian geometry include Finsler geometry.

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.

Point Line segment ray Length. It deals with a broad range of geometries whose metric properties vary from point to point, including riemannidnne standard types of Non-Euclidean geometry.

Two-dimensional Plane Area Polygon. Views Read Edit View history. From those, some other global quantities can be derived by integrating local contributions. Brans—Dicke theory Kaluza—Klein Quantum gravity. Altitude Hypotenuse Pythagorean theorem.

Riemannian geometry is the branch of differential geometry that studies Riemannian manifoldssmooth manifolds with a Riemannian metrici. By using this site, you agree to the Terms of Use and Privacy Policy. Most of the results can be found in the classic monograph by Jeff Cheeger and D.

Projecting a ruemannienne to a plane.