Riemannian
Encyclopedia
Riemannian most often refers to Bernhard Riemann
Bernhard Riemann
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....

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  • Riemannian geometry
    Riemannian geometry
    Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives, in particular, local notions of angle, length...

  • Riemannian manifold
    Riemannian manifold
    In Riemannian geometry and the differential geometry of surfaces, a Riemannian manifold or Riemannian space is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, which varies smoothly from point to point...

    • Pseudo-Riemannian manifold
      Pseudo-Riemannian manifold
      In differential geometry, a pseudo-Riemannian manifold is a generalization of a Riemannian manifold. It is one of many mathematical objects named after Bernhard Riemann. The key difference between a Riemannian manifold and a pseudo-Riemannian manifold is that on a pseudo-Riemannian manifold the...

    • Sub-Riemannian manifold
      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 subspaces....

    • Riemannian submanifold
      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 is a Riemannian submanifold....

    • Riemannian metric
  • Riemannian circle
    Riemannian circle
    In metric space theory and Riemannian geometry, the Riemannian circle is a great circle equipped with its great-circle distance...

  • Riemannian submersion
    Riemannian submersion
    In differential geometry, a branch of mathematics, a Riemannian submersion is a submersion from one Riemannian manifold to another that respects the metrics, meaning that it is an orthogonal projection on tangent spaces....

  • Riemannian Penrose inequality
    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 Riemannian Penrose inequality is the most important special...

  • Riemannian holonomy
  • Riemann curvature tensor
    Riemann curvature tensor
    In the mathematical field of differential geometry, the Riemann curvature tensor, or Riemann–Christoffel tensor after Bernhard Riemann and Elwin Bruno Christoffel, is the most standard way to express curvature of Riemannian manifolds...

  • Riemannian connection
    • Riemannian connection on a surface
      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 transport, covariant derivative and connection form...

  • Riemannian symmetric space
    Riemannian symmetric space
    In differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to formulate the inversion symmetry, via Riemannian geometry or via Lie theory...

  • Riemannian volume form
  • Riemannian bundle metric
  • List of topics named after Bernhard Riemann


but may also refer to Hugo Riemann
Hugo Riemann
Karl Wilhelm Julius Hugo Riemann was a German music theorist.-Biography:Riemann was born at Grossmehlra, Schwarzburg-Sondershausen. He was educated in theory by Frankenberger, studied the piano with Barthel and Ratzenberger, studied law, and finally philosophy and history at Berlin and Tübingen...

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  • Neo-Riemannian theory
    Neo-Riemannian theory
    Neo-Riemannian theory refers to a loose collection of ideas present in the writings of music theorists such as David Lewin, Brian Hyer, Richard Cohn, and Henry Klumpenhouwer...

    (music)
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