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]
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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.
Riemanninvariants are mathematical transformations made on a system of conservation equations to make them more easily solvable. Riemanninvariants are...
Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces...
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...
field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the...
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...
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the...
the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of...
state. In the language of Riemanninvariant, the simple wave can also be defined as the zone where one of the Riemanninvariant is constant in the region...
Principle of mutability Conservation law of the Stress–energy tensor Riemanninvariant Philosophy of physics Totalitarian principle Convection–diffusion...
over the Riemann surface M. Then a Higgs bundle ( E , φ ) {\displaystyle (E,\varphi )} is stable if, for each φ {\displaystyle \varphi } invariant subbundle...
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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known since Riemann that the algebraic variety condition imposes extra constraints on a complex torus. The following criterion by Riemann decides whether...
give the same surface. Therefore, the Riemann surface, or more simply its Geometric genus is a birational invariant. A more complicated example is given...
expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from...
orientability (a normal invariant, also detected by homology) and genus (a homological invariant). Smooth closed manifolds have no local invariants (other than dimension)...
compact, semi-simple Lie groups equipped with a bi-invariant Riemannian metric. Every compact Riemann surface of genus greater than 1 (with its usual metric...
considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. The following are basic...
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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