- Riemann manifold
- = Riemannian manifold риманово многообразие
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Riemann manifold
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Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… … Wikipedia
Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… … Wikipedia
Riemann sphere — The Riemann sphere can be visualized as the complex number plane wrapped around a sphere (by some form of stereographic projection – details are given below). In mathematics, the Riemann sphere (or extended complex plane), named after the 19th… … Wikipedia
Riemann curvature tensor — In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor is the most standard way to express curvature of Riemannian manifolds. It is one of many things named after Bernhard Riemann and Elwin… … Wikipedia
Riemann-Roch theorem for smooth manifolds — In mathematics, a Riemann Roch theorem for smooth manifolds is a version of results such as the Hirzebruch Riemann Roch theorem or Grothendieck Riemann Roch theorem (GRR) without a hypothesis making the smooth manifolds involved carry a complex… … Wikipedia
Riemann, Bernhard — ▪ German mathematician in full Georg Friedrich Bernhard Riemann born September 17, 1826, Breselenz, Hanover [Germany] died July 20, 1866, Selasca, Italy German mathematician whose profound and novel approaches to the study of geometry laid the … Universalium
Riemann mapping theorem — In complex analysis, the Riemann mapping theorem states that if U is a simply connected open subset of the complex number plane Bbb C which is not all of Bbb C, then there exists a biholomorphic (bijective and holomorphic) mapping f, from U, onto … Wikipedia
Riemann tensor (general relativity) — The Riemann tensor (general relativity) is a mathematical object that describes gravitation and its effects in Einstein s theory of general relativity. Curvature and geodesic deviationThe Riemann tensor can be used to express the idea of… … Wikipedia
Riemann–Hilbert correspondence — In mathematics, the Riemann Hilbert correspondence is a generalization of Hilbert s twenty first problem to higher dimensions. The original setting was for Riemann surfaces, where it was about the existence of regular differential equations with… … Wikipedia
Riemann surface — noun a one dimensional complex manifold; a generalization of the complex plane … Wiktionary
Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… … Wikipedia
