Takree 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. There was a problem providing the content you requested 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.

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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. In other projects Wikimedia Commons. Riemannian geometry — Wikipedia This list is oriented to those who already know the basic definitions and want to know what these definitions are about.

Dislocations and Disclinations produce torsions and curvature. Point Line segment ray Length. Any smooth manifold admits a Riemannian metricwhich often helps to solve problems of differential topology. Volume Cube cuboid Cylinder Pyramid Sphere. What follows is an incomplete list of the most classical theorems in Riemannian geometry.

It deals with a broad range of geometries whose metric properties vary from point to point, including the standard types of Non-Euclidean geometry.

It is a very broad and abstract generalization of the differential geometre of surfaces in R 3. Two-dimensional Plane Area Polygon.

Introduction History Mathematical formulation Tests. From Wikipedia, the free encyclopedia. Projecting a sphere to a plane. This page was last edited on 30 Decemberat The choice is made depending on its importance and elegance of formulation. Brans—Dicke theory Kaluza—Klein Quantum gravity.

Kaluza—Klein theory Quantum gravity Supergravity. Views Read Edit View history. Other generalizations of Riemannian geometry include Finsler geometry. From those, some other global quantities can be derived by integrating local contributions.

Riemannian geometry Bernhard Riemann. The formulations given riemannienje far from being very exact or the most general. 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.

Riemannian geometry was first put forward in generality by Bernhard Riemann in the 19th century. Geometriie geometry is the branch of differential geometry that studies Riemannian manifoldssmooth manifolds with a Riemannian metrici. This gives, in particular, local notions of anglelength of curvessurface area and volume. Most of the iremannienne 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.

Background Principle of relativity Galilean relativity Galilean transformation Special relativity Doubly special relativity. 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 Background Introduction Mathematical formulation. Altitude Hypotenuse Pythagorean theorem. Time dilation Mass—energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Ladder paradox Twin paradox. 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.

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