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1. Curvature of Riemannian manifolds: In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous way to define curvature ... [100%] 2023-10-22 [Curvature (mathematics)] [Differential geometry]...

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1. 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. (Type of generalization of a Riemannian manifold) [100%] 2023-08-18 [Metric geometry] [Riemannian geometry]...
2. Pseudo-Riemannian manifold: In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness ... (Differentiable manifold with nondegenerate metric tensor) [100%] 2024-03-02 [Differential geometry] [Lorentzian manifolds]...
3. Manifold: MANIFOLD man'-i-fold (rabh; poikilos): "Manifold," which occurs only a few times, is in the Old Testament the translation of rabh, "many," "abundant" (Nehemiah 9:19,27; Amos 5:12, where it is equivalent to "many"), and of rabhabh ... [75%] 1915-01-01
4. Manifold: An n-dimensional manifold (or n-manifold) M is a topological space such that every point in M has a neighbourhood that is homeomorphic to . These homeomorphisms induce a coordinatization of M, and it is further required that the coordinatization ... [75%] 2023-03-06 [Topology] [Mathematics]...
5. Manifold (geometry): A manifold is an abstract mathematical space that looks locally like Euclidean space, but globally may have a very different structure. An example of this is a sphere: if one is very close to the surface of the sphere, it ... (Geometry) [75%] 2023-07-04
6. Manifold (fluid mechanics): A manifold is a wide and/or bigger pipe, or channel, into which smaller pipes or channels lead. A pipe fitting or similar device that connects multiple inputs or outputs. (Physics) [75%] 2023-11-27 [Fluid mechanics]
7. Manifold: A geometric object which locally has the structure (topological, smooth, homological, etc.) of $ \mathbf R ^ {n} $ or some other vector space. This fundamental idea in mathematics refines and generalizes, to an arbitrary dimension, the notions of a line and a ... (Mathematics) [75%] 2023-11-26
8. Manifold (prediction market): Manifold, formerly known as Manifold Markets, is a reputation-based prediction market. Users compete with other users, betting on various topics, from natural disasters like hurricanes to political events. (Finance) [75%] 2024-02-27 [Prediction markets]
9. Manifold (prediction market): Manifold, formerly known as Manifold Markets, is an online prediction market platform. Users engage in competitive forecasting using play money called 'mana'. (Prediction market) [75%] 2024-02-14
10. Riemannian domain: Riemann domain, complex (-analytic) manifold over $ \mathbf C ^{n} $ An analogue of the Riemann surface of an analytic function $ w = f(z) $ of a single complex variable $ z $ for the case of analytic functions $ w = f(z) $, $ z = (z _ ... (Mathematics) [69%] 2023-10-27
11. Riemannian connection: An affine connection on a Riemannian space $ M $ with respect to which the metric tensor $ g _ {ij} $ of the space is covariantly constant. If the affine connection on $ M $ is given by a matrix of local connection forms $$ \tag ... (Mathematics) [69%] 2023-10-27
12. 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 2π, or the extrinsic ... [69%] 2023-01-16 [Riemannian geometry] [Circles]...
13. Riemannian geometry: Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). This gives, in ... (Branch of differential geometry) [69%] 2023-09-14 [Riemannian geometry]
14. Riemannian geometry: Riemmanian geometry is a non-euclidean geometric theory developed by mathematicians Bernhard Riemann and Carl Friedrich Gauss, and was later used in the Theory of Relativity. It is not as simple as euclidean geometry since it is not as close ... [69%] 2023-02-10 [Cosmology] [Mathematics]...
15. Riemannian curvature: A measure of the difference between the metrics of a Riemannian and a Euclidean space. Let $ M $ be a point of a Riemannian space and let $ F $ be a two-dimensional regular surface $ x ^ {i} = x ^ {i} ( u, v) $ passing ... (Mathematics) [69%] 2023-08-20
16. Riemannian geometry: The theory of Riemannian spaces. A Riemannian space is an -dimensional connected differentiable manifold on which a differentiable tensor field of rank 2 is given which is covariant, symmetric and positive definite. (Mathematics) [69%] 2023-10-19
17. Riemannian theory: Riemannian theory, in general, refers to the musical theories of German theorist Hugo Riemann (1849–1919). His theoretical writings cover many topics, including musical logic, notation, harmony, melody, phraseology, the history of music theory, etc. (Musical theories of Hugo Riemann) [69%] 2023-12-14 [Riemannian theory] [Diatonic functions]...
18. Riemannian space: A space in small domains of which the Euclidean geometry is approximately valid (up to infinitesimals of an order higher than the dimensions of the domains), though in the large such a space may be non-Euclidean. Such a space ... (Mathematics) [69%] 2023-09-13
19. Riemannian metric: The metric of a space given by a positive-definite quadratic form. If a local coordinate system $ ( x ^ {1} \dots x ^ {n} ) $ is introduced for the space $ V _ {n} $ and if at each point $ X( x ^ {1} \dots x ... (Mathematics) [69%] 2023-09-01