Riemannian geometry
- noun
- /riˈmɑːniən dʒiˈɒmɪtri/
- Specialized
:
geometría riemanniana
- The tensor, in Riemannian geometry, measures the curvature of the space; that is, the deviation of the space from being flat.
Examples
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In Riemannian geometry, mathematicians analyze how the curvature of space differs from flat geometries.
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The field of Riemannian geometry explores the properties of curved spaces, similar to the surface of a sphere.
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If (3.7) reduces to the ordinary geodesic of Riemannian geometry.
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To me, the one that sticks out like a sore thumb is the assumption that space-time is differentiable, the whole basis of Riemannian geometry.
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For example, the geodesic equation of Riemannian geometry is used as the equation of motion of a test particle (e.g., planet) in the solar system, in the context of GR.
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Straight lines in Riemannian geometry are represented by great circles, demonstrating how they curve on a sphere.
Surface Forms
Morphology
This is a straightforward adjective + noun composition: if a learner knows 'Riemannian' (meaning geometry for curved spaces) and 'geometry', the combined meaning is directly derivable as the type of geometry described by Riemann. Although technical and low-frequency, the semantic contribution of each constituent is transparent and follows normal adjectival modification patterns.
Etymology
Riemannian geometry is named after the mathematician Bernhard Riemann and grew from his idea of studying geometry on curved surfaces like a sphere. Imagine the shortest path on a globe is a curved 'straight line' called a great circle. So Riemannian geometry now means the 'geometry of curved spaces' and is used in physics such as Einstein's theory.
