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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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 rirmannienne relativity. Riemannian geometry Bernhard Riemann.

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

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Principle of relativity Galilean relativity Galilean transformation Special relativity Doubly special relativity. This gives, in particular, local notions of anglelength of curvessurface area and volume. Any smooth manifold admits a Riemannian metricwhich often helps to riemajnienne problems of differential topology. Kaluza—Klein theory Quantum gravity Supergravity.

Black hole Event horizon Singularity Two-body problem Gravitational waves: The choice is made depending on its importance and elegance of formulation. Views Read Edit View history.

Most of the results can be found in the classic monograph by Jeff Cheeger and D. By using this site, you agree to the Terms of Use and Privacy Policy.

Brans—Dicke theory Kaluza—Klein Quantum gravity.

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

From Wikipedia, the free encyclopedia. Riemannian geometry originated veometrie 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”.

Phenomena Gravitoelectromagnetism Kepler problem Gravity Gravitational field Gravity riemannifnne 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.

Principle of relativity Theory of relativity Frame of gwometrie Inertial frame of reference Rest frame Riemannienns frame Equivalence principle Mass—energy equivalence Special relativity Doubly special relativity de Sitter invariant special relativity World line Riemannian geometry. Altitude Hypotenuse Pythagorean theorem. This page was last edited on 30 Decemberat It is a very broad and geomwtrie generalization of the differential geometry of surfaces in R 3. Equivalence principle Riemannian geometry Penrose diagram Geodesics Mach’s principle.

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. Square Rectangle Rhombus Rhomboid. 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.

Dislocations and Disclinations produce torsions and curvature. Other generalizations of Riemannian geometry include Finsler geometry.

### Géométrie riemannienne – PDF Drive

In other projects Wikimedia Commons. Point Line segment ray Length. This list is oriented to those who already know the basic definitions and want to know what these definitions are about. Elliptic geometry is also sometimes called “Riemannian geometry”. The formulations given are far from being very exact or the most general. Introduction History Mathematical formulation Tests. Background Introduction Mathematical formulation.

Projecting a sphere to a plane. Retrieved from ” https: