Riemannian geometry


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Rie·mann·ian geometry

 (rē-män′ē-ən)
n.
A non-Euclidean system of geometry based on the postulate that within a plane every pair of lines intersects.

[After Georg Friedrich Bernhard Riemann.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Riemannian geometry

n
(Mathematics) a branch of non-Euclidean geometry in which a line may have many parallels through a given point. It has a model on the surface of a sphere, with lines represented by great circles. Also called: elliptic geometry
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

Riemann′ian geom′etry


n.
the branch of non-Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that in a plane every pair of distinct lines intersects.
[1915–20; after German.French.B. Riemann]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.Riemannian geometry - (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"
math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
non-Euclidean geometry - (mathematics) geometry based on axioms different from Euclid's; "non-Euclidean geometries discard or replace one or more of the Euclidean axioms"
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
References in periodicals archive ?
Thomas presents her lecture notes for a graduate course for students with a background in basic group theory including group actions, a first course in algebraic topology, and some familiarity with Riemannian geometry, particularly the geometry of the hyperbolic plane.
P.Eisenhart, Riemannian Geometry, Princeton University Press, 1949.
Although Einstein's general relativity described by Riemannian geometry is one of the most successful gravitational theories, it still has some problems in explaining the accelerating expansion of the universe and establishing a complete theory of quantum gravity.
Riemannian geometry gives us the Gauss-Weingarten equations along the sub-manifold N of the Riemannian manifold (M, [psi]),
The features are extracted by using the Riemannian geometry [14], which manipulates the covariance matrices of the MEG signals.
Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, Volume 203, Birkhauser, 2002.
Sakai, Riemannian geometry, translated from the 1992 Japanese original by the author, Translations of Mathematical Monographs, 149, Amer.
Arimoto, "Modeling and control of multi-body mechanical systems: part i a riemannian geometry approach," in Advances in the Theory of Control, Signals and Systems with Physical Modeling, vol.
Since then his work has been used in resolving many longstanding open problems in Riemannian geometry and 3-dimensional topology.
Contact manifolds in riemannian geometry. Berlin-New York: Lecture Notes in Mathematics, Springer-Verlag 509, 1976.