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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Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach’s principle. It deals with a broad range of geometries whose metric properties vary from point to point, including the standard types of Non-Euclidean geometry. Introduction History Mathematical formulation Tests. By using this site, you agree to the Terms of Use and Privacy Policy. 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”.

This gives, in particular, local notions of anglelength of curvessurface area and volume. From those, some other global quantities can be derived by integrating local contributions. Other generalizations of Riemannian gepmetrie include Finsler geometry.

Géométrie riemannienne – PDF Drive

Most of the results can be found in the classic monograph by Jeff Cheeger and D. 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. Principle of relativity Galilean relativity Galilean transformation Special relativity Doubly special relativity.

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Light cone World line Minkowski diagram Biquaternions Minkowski space. In other projects Wikimedia Commons. Black hole Event horizon Singularity Two-body problem Gravitational waves: Retrieved from ” https: 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.

From Wikipedia, the free encyclopedia. Altitude Hypotenuse Pythagorean theorem. Background Introduction Mathematical formulation. Brans—Dicke theory Kaluza—Klein Quantum gravity. Dislocations and Disclinations produce torsions and curvature.

Two-dimensional Plane Area Polygon. Point Line segment ray Length.

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. There exists a close analogy of differential geometry with the mathematical structure of defects in regular crystals.

Riemannian geometry is the branch of differential geometry that studies Riemannian manifoldssmooth manifolds with a Riemannian metrici.

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

Volume Cube cuboid Cylinder Pyramid Sphere. This list is oriented to those who already know the basic definitions and want to know what these definitions are about. The formulations given are far from being very exact or the most general.

Riemannian geometry

Square Rectangle Rhombus Rhomboid. Views Read Edit View history. It is a very broad and abstract generalization of the differential geometry of surfaces in R 3. Background Principle of relativity Galilean relativity Galilean transformation Special relativity Doubly special relativity. Any smooth manifold admits a Riemannian metricwhich often helps to solve problems of differential topology. Riemannian geometry was first put forward in generality by Bernhard Geometeie in the 19th century.

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Projecting a sphere to a plane. Kaluza—Klein theory Quantum gravity Supergravity. Elliptic geometry is also sometimes called “Riemannian geometry”. 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.

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 Geonetrie collapse Frame-dragging Geodetic effect Gravitational singularity Event horizon Naked singularity Black hole White hole.

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.

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

Time dilation Mass—energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Ladder paradox Twin paradox. Riemannian geometry Bernhard Riemann.

What follows is an incomplete list of the most classical theorems in Riemannian geometry.