The German mathematician

Bernhard Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rig ...

(1826–1866) is the eponym of many things.

"Riemann" (by field)

Riemann bilinear relations In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: * A lattice Λ in a complex vector space Cg. * An alternating bilinear form α from Λ to the integers satisfying the following Riemann bi ...

* Riemann conditions *

Riemann form In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: * A lattice Λ in a complex vector space Cg. * An alternating bilinear form α from Λ to the integers satisfying the following Riemann bili ...

* Riemann function * Riemann–Hurwitz formula * Riemann matrix * Riemann operator * Riemann singularity theorem ** Riemann-Kempf singularity theorem * Riemann surface ** Compact Riemann surface ** Planar Riemann surface * Cauchy–Riemann manifold ** The tangential Cauchy–Riemann complex *

Zariski–Riemann space In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring ''k'' of a field ''K'' is a locally ringed space whose points are valuation rings containing ''k'' and contained in ''K''. They generalize the Riemann surface of a c ...

Analysis

* Cauchy–Riemann equations * Riemann integral ** Generalized Riemann integral ** Riemann multiple integral *

Riemann invariant 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 obta ...

* Riemann mapping theorem ** Measurable Riemann mapping theorem * Riemann problem * Riemann solver * Riemann sphere * Riemann–Hilbert correspondence *

Riemann–Hilbert problem In mathematics, Riemann–Hilbert problems, named after Bernhard Riemann and David Hilbert, are a class of problems that arise in the study of differential equations in the complex plane. Several existence theorems for Riemann–Hilbert problems h ...

* Riemann–Lebesgue lemma * Riemann–Liouville integral * Riemann–Roch theorem **

Arithmetic Riemann–Roch theorem In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine equations in higher dimensions. Background The main motivation behind Arakelov geometry is th ...

** Riemann–Roch theorem for smooth manifolds ** Riemann–Roch theorem for surfaces ** Grothendieck–Hirzebruch–Riemann–Roch theorem ** Hirzebruch–Riemann–Roch theorem * Riemann–Stieltjes integral * Riemann series theorem * Riemann sum

Number theory

* Riemann–von Mangoldt formula *

Riemann hypothesis 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 with real part . Many consider it to be the most important unsolved problem in ...

** Generalized Riemann hypothesis ** Grand Riemann hypothesis **

Riemann hypothesis for curves over finite fields In number theory, the local zeta function (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as :Z(V, s) = \exp\left(\sum_^\infty \frac (q^)^m\right) where is a non-singular -dimensional projective algeb ...

Riemann theta function In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theo ...

* Riemann Xi function *

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > ...

* Riemann–Siegel formula * Riemann–Siegel theta function

Physics

Free Riemann gas In mathematical physics, the primon gas or free Riemann gas is a toy model illustrating in a simple way some correspondences between number theory and ideas in quantum field theory and dynamical systems. It is a quantum field theory of a set of non ...

also called primon gas *

* Riemann–Cartan geometry * Riemann–Silberstein vector * Riemann-Lebovitz formulation * Riemann curvature tensor also called Riemann tensor * Riemann tensor (general relativity)

Riemannian

* Pseudo-Riemannian manifold *

Riemannian bundle metric In differential geometry, the notion of a metric tensor can be extended to an arbitrary vector bundle, and to some principal fiber bundles. This metric is often called a bundle metric, or fibre metric. Definition If ''M'' is a topological manifold ...

Riemannian circle In metric space theory and Riemannian geometry, the Riemannian circle is a great circle with a characteristic length. It is the circle equipped with the ''intrinsic'' Riemannian metric of a compact one-dimensional manifold of total length 2, or ...

* Riemannian cobordism * Riemannian connection *

Riemannian connection on a surface In mathematics, the Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Élie Cartan and Hermann Weyl in the early part of the twentieth century: parallel t ...

* Riemannian cubic * Riemannian cubic polynomials * Riemannian foliation * Riemannian geometry ** Fundamental theorem of Riemannian geometry * Riemannian graph * Riemannian group * Riemannian holonomy *

Riemannian manifold In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real manifold, real, smooth manifold ''M'' equipped with a positive-definite Inner product space, inner product ...

also called Riemannian space * Riemannian metric tensor *

Riemannian Penrose inequality In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem. The Riemannia ...

* Riemannian polyhedron * Riemannian singular value decomposition *

Riemannian submanifold A Riemannian submanifold ''N'' of a Riemannian manifold ''M'' is a submanifold of ''M'' equipped with the Riemannian metric inherited from ''M''. The image of an isometric immersion In mathematics, an embedding (or imbedding) is one instance of ...

* Riemannian submersion * Riemannian volume form * Riemannian wavefield extrapolation *

Sub-Riemannian manifold In mathematics, a sub-Riemannian manifold is a certain type of generalization of a Riemannian manifold. Roughly speaking, to measure distances in a sub-Riemannian manifold, you are allowed to go only along curves tangent to so-called ''horizontal ...

Riemannian symmetric space In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, ...

Riemann's

Riemann's differential equation In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points to occur anywhere on the Riemann sphere, rather than merely at 0, ...

Riemann's existence theorem In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by ...

Riemann's explicit formula In mathematics, the explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by for the Riemann zeta function. Such explicit formulae have been applied ...

Riemann's minimal surface In differential geometry, Riemann's minimal surface is a one-parameter family of minimal surfaces described by Bernhard Riemann in a posthumous paper published in 1867. Surfaces in the family are singly periodic minimal surfaces with an infinite ...

* Riemann's theorem on removable singularities

Non-mathematical

Riemann (crater) Riemann (pronounced ''REE mahn'') is a lunar impact crater that is located near the northeastern limb of the Moon, and can just be observed edge-on when libration effects bring it into sight. It lies to the east-northeast of the large walled plain ...

* 4167 Riemann {{DEFAULTSORT:List Of Topics Named After Bernhard Riemann Riemann Bernhard Riemann