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Riemann invariant information


Riemann invariants are mathematical transformations made on a system of conservation equations to make them more easily solvable. Riemann invariants are constant along the characteristic curves of the partial differential equations where they obtain the name invariant. They were first obtained by Bernhard Riemann in his work on plane waves in gas dynamics.[1]

  1. ^ Riemann, Bernhard (1860). "Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite" (PDF). Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen. 8. Retrieved 2012-08-08.

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Riemann invariant

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Riemann invariants are mathematical transformations made on a system of conservation equations to make them more easily solvable. Riemann invariants are...

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Riemann surface

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Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces...

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List of things named after Bernhard Riemann

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Riemann hypothesis

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In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers...

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Riemann integral

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the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of...

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Riemann curvature tensor

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field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the...

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Riemann sphere

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In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the...

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Simple wave

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state. In the language of Riemann invariant, the simple wave can also be defined as the zone where one of the Riemann invariant is constant in the region...

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Kretschmann scalar

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completely traceless part of the Riemann tensor. In d {\displaystyle d} dimensions this is related to the Kretschmann invariant by R a b c d R a b c d = C a...

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Geometric invariant theory

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In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli...

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Conservation law

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Principle of mutability Conservation law of the Stress–energy tensor Riemann invariant Philosophy of physics Totalitarian principle Convection–diffusion...

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Geometric genus

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In algebraic geometry, the geometric genus is a basic birational invariant pg of algebraic varieties and complex manifolds. The geometric genus can be...

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Lorentz scalar

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expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from...

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Birational invariant

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give the same surface. Therefore, the Riemann surface, or more simply its Geometric genus is a birational invariant. A more complicated example is given...

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Manifold

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orientability (a normal invariant, also detected by homology) and genus (a homological invariant). Smooth closed manifolds have no local invariants (other than dimension)...

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Abelian variety

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known since Riemann that the algebraic variety condition imposes extra constraints on a complex torus. The following criterion by Riemann decides whether...

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Geometric function theory

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entitled to do since the Euler characteristic is a topological invariant. What the Riemann–Hurwitz formula does is to add in a correction to allow for ramification...

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Curvature invariant

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geometry, curvature invariants are scalar quantities constructed from tensors that represent curvature. These tensors are usually the Riemann tensor, the Weyl...

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