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Geodesic

In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line".

Applications, Examples of applications & Affine geodesics

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Overview

Introduction

Metric geometry

Riemannian geometry

Affine geodesics

Computational methods

Ribbon test

Examples of applications

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Geodesic

Nodes166
Edges165
Triples184
Avg. degree1.99
Density0.012048
Components1

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Geodesic

Top relations

related to Further reading · 65
Geodesic → Abraham, Adler, Applications, Bazin, Benjamin-Cummings, Berlin, Bibcode, Cambridge University Press, Charles, Classical Theory, Cosmology, Differential Geometry, EMS Press, Encyclopedia, Fields, Foundations, Freeman, General Relativity, General Theory, Geometric Analysis
see also · 12
Geodesic → Analyzes, Concept, Formula, Gives, Introduction, Line, Recreational, Riemannian, Rinow, Study, Surface, Vector
related to Topology and geometric group theory · 11
Geodesic → CAT, Euler, For, Gromov-hyperbolicity, Hopf-Rinow, In, Milnor, Morse, Riemannian, These, They
related to Existence and uniqueness · 7
Geodesic → Existence, Lindelöf, More, ODE, ODEs, Picard, The
related to Heat method · 7
Geodesic → Because, Crane, Poisson, The, Varadhan's, Wardetzky's, Weischedel
related to Introduction · 7
Geodesic → Equivalently, In, Intuitively, It, Riemannian, The, This
related to Mitchell–Mount–Papadimitriou algorithm · 7
Geodesic → Dijkstra, Dijkstra's, Mitchell, MMP, Mount, Papadimitriou, Their
related to Engineering · 6
Geodesic → Earth, Geodesics, GSP, Poisson, Shortest, UV
related to External links · 6
Geodesic → Archived, Geodesics Revisited, Introduction, Manifold Atlas, Totally, Wayback Machine
related to Examples · 5
Geodesic → Euclidean, Geodesics, If, On, The

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Important terminology

geodesics displaystyle riemannian distance metric connection curve points manifold surface geometry two gamma shortest equation vector path general point along

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Geodesicis acurve which is everywhere locally a distance minimizer0.90text
the Kullback-Leibler divergence play a role analogous to that of a Riemannian metricinstance ofdivergences0.80text
allowing analogies for connectionsinstance ofdivergences0.80text
geodesics.PhysicsIn classical mechanicsinstance ofdivergences0.80text
trajectories minimize an energy according to the Hamilton-Jacobi equationinstance ofdivergences0.80text
which can be regarded as a similar idea to geodesicsinstance ofdivergences0.80text
geodesicsinstance ofdivergences0.80text
Geodesichas methodEfficient0.60section
Geodesicrelated to Affine and projective geodesicsEquation0.60section
Geodesicrelated to Affine and projective geodesicsThus0.60section
Geodesicrelated to Affine and projective geodesicsAccordingly0.60section
Geodesicrelated to Affine geodesicsMore0.60section

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