Riemannian
- adjective
- /riˈmɑːniən/
- Specialized
:
riemanniano
- Today's goal is to get to the curvature tensor of a Riemannian geometry.
Minkowski space, Riemannian geometry, the Ricci tensor, Lorentz symmetry, the Poincare group.
- Minkowski space, Riemannian geometry, the Ricci tensor, Lorentz symmetry, the Poincare group.
Examples
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So space-time is curvature, the study of Riemannian manifolds and curvature and differential geometry.
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I think we want to start with the mathematics of Euclidean of of Riemannian geometry.
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OK, so I just explained to you that's the basis of Riemannian geometry, which luckily for Einstein, Riemann had worked it up web work go out.
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They think it's variably curved Riemannian manifold, and so So what that means is that you vary the curvature from point to point.
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Minkowski space, Riemannian geometry, the Ricci tensor, Lorentz symmetry, the Poincare group.
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The concepts of curvature and distance are key in Riemannian geometry.
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In Riemannian geometry, the angles of a triangle can add up to more than 180 degrees.
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Researchers study the properties of Riemannian manifolds to understand curved spaces in physics.
Compounds
- Specialized
A way to study curved space, like a sphere, where straight lines are like great circles
Surface Forms
Morphology
Riemannian = Riemann (semi-transparent) = Riemann + ian
Formed regularly from the proper name 'Riemann' + the adjectival suffix '-ian' meaning 'relating to', but the specific technical meaning (a particular type of geometry) is specialized and not inferable by learners unfamiliar with Riemann.
Etymology
Riemannian comes from the name Riemann, the German mathematician Bernhard Riemann, and the ending -ian which means 'related to' or 'belonging to', like in Newtonian. The word names the kind of geometry he developed, so Riemannian geometry means geometry 'related to' Riemann's ideas about curved space and how to measure distances on curved surfaces.
