Definitions for riemannian geometry
rie·mann·ian ge·om·e·t·ry

Princeton's WordNetRate this definition:0.0 / 0 votes

1. elliptic geometry, Riemannian geometrynoun

   (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle

   "Bernhard Riemann pioneered elliptic geometry"

WiktionaryRate this definition:0.0 / 0 votes

1. Riemannian geometrynoun

   the branch of differential geometry that studies Riemannian manifolds

2. Etymology: Riemannian + geometry

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1. riemannian geometry

   Riemannian geometry is a branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric. This is a real, symmetric, positive-definite bilinear form on each tangent space. This gives a natural notion of length of vectors and angle between vectors which varies smoothly from point to point, enabling calculations of curvature, gradients, and other concepts that have a geometric interpretation in the physical world. This type of geometry is named after the German mathematician Bernhard Riemann. Its study is fundamental in the fields of physics, particularly in the theory of general relativity.

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1. 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 of curves, surface area, and volume. From those some other global quantities can be derived by integrating local contributions. Riemannian geometry originated with the vision of Bernhard Riemann expressed in his inaugurational lecture Ueber die Hypothesen, welche der Geometrie zu Grunde liegen. It is a very broad and abstract generalization of the differential geometry of surfaces in R³. Development of Riemannian geometry resulted in synthesis of diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable manifolds of higher dimensions. It enabled Einstein's general relativity theory, made profound impact on group theory and representation theory, as well as analysis, and spurred the development of algebraic and differential topology.

Matched Categories

1. • Mathematics
   • Non-Euclidean Geometry

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Numerology

1. Chaldean Numerology

   The numerical value of riemannian geometry in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of riemannian geometry in Pythagorean Numerology is: 8

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=riemannian geometry
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Riemannian_Geometry
3. ^ ChatGPT
   https://chat.openai.com
4. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=riemannian geometry