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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This list is oriented to those who already know the basic definitions and want to know what these definitions are about.

### Géométrie riemannienne en dimension 4 : Séminaire Arthur Besse /79 in SearchWorks catalog

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

Black hole Event horizon Singularity Two-body problem Gravitational waves: Most of the results can be found in the classic monograph by Jeff Cheeger and D. Views Read Edit View history.

### Géométrie riemannienne – PDF Drive

Riemannian geometry Bernhard Riemann. It is a very broad and abstract generalization of the differential geometry of surfaces in R 3. Other generalizations of Riemannian geometry include Finsler geometry. Phenomena Gravitoelectromagnetism Kepler problem Gravity Gravitational field Gravity well Gravitational lensing Gravitational waves Gravitational redshift Redshift Blueshift Time dilation Gravitational time riemannenne Shapiro time delay Gravitational potential Gravitational compression Gravitational collapse Frame-dragging Geodetic effect Gravitational singularity Event horizon Naked singularity Black hole White hole.

This gives, in particular, local notions of anglelength of curvessurface area and volume.

The formulations given are far from being very exact or the most general. In other projects Wikimedia Commons. It deals with a broad range of geometries whose metric properties vary from point to point, including the standard types of Non-Euclidean geometry. 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”.

Any smooth manifold admits a Riemannian metricwhich often helps to solve problems of differential topology. Kaluza—Klein theory Quantum gravity Supergravity. There exists a close analogy of differential geometry with the mathematical structure of defects in regular crystals.

This page was last edited on 30 Decemberat Volume Cube cuboid Cylinder Pyramid Sphere. Time dilation Mass—energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas riemamnienne Ladder paradox Twin paradox. Introduction History Mathematical formulation Tests. Equivalence principle Riemannian riemxnnienne Penrose diagram Geodesics Mach’s principle.

What follows is an incomplete list of the most classical theorems in Riemannian geometry. By using this site, you agree to the Terms of Use and Privacy Policy.

It also serves as an entry level for the riemanniene complicated rlemannienne of pseudo-Riemannian manifoldswhich in four dimensions are the main objects of the theory of general relativity. Dislocations and Disclinations produce torsions and curvature.

Two-dimensional Plane Area Polygon. 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.

Altitude Hypotenuse Pythagorean theorem. Square Rectangle Rhombus Rhomboid.

The choice is made depending on its importance and elegance of 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.

Background Introduction Mathematical formulation. Brans—Dicke theory Kaluza—Klein Quantum gravity. Light cone World line Minkowski diagram Biquaternions Minkowski space. Point Line segment ray Length.

Projecting a sphere to a plane. Principle of relativity Galilean relativity Galilean transformation Special relativity Doubly special relativity. 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.

From those, some other global quantities can be derived by integrating local contributions. Retrieved from ” https: 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 Principle of relativity Galilean relativity Galilean transformation Special relativity Doubly special relativity.

## Variété pseudo-riemannienne

From Wikipedia, the free encyclopedia. Elliptic geometry is also sometimes called “Riemannian geometry”. Riemannian geometry is the branch of differential geometry that studies Riemannian manifoldssmooth manifolds with a Riemannian metrici.