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Differential geometry of surfaces

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric.

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Overview

History

Regular surfaces in Euclidean space

Examples

Local metric structure

Geodesic curves on a surface

Geodesic polar coordinates

Gauss–Bonnet theorem

Surfaces of constant curvature

Riemannian connection and parallel transport

Global differential geometry of surfaces

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Map overview Semantic statistics

Differential geometry of surfaces

Nodes285
Edges284
Triples26
Avg. degree1.99
Density0.007018
Components1

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Differential geometry of surfaces

Top relations

related to Riemannian connection and parallel transport · 7
Differential geometry of surfaces → Bernhard Riemann, Cartan, Gauss, Hermann Weyl, Riemannian, The, Tullio Levi-Civita
related to Geodesic curves on a surface · 6
Differential geometry of surfaces → Curves, Euclidean, It, Mathematically, Riemannian, The
related to External links · 4
Differential geometry of surfaces → Differential, Media, Wikimedia Commons, Wiktionary-logo-en-v2

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Important terminology

surface curvature surfaces geodesic gauss differential given gaussian geometry vector point two space plane tangent isbn metric first one local

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
planesinstance offamiliar examples0.80text
cylindersinstance offamiliar examples0.80text
and spheresminimal surfacesinstance offamiliar examples0.80text
which are defined by the property that their mean curvature is zero at every pointinstance offamiliar examples0.80text
cuspidal edgesinstance ofS may have singularities0.80text
the Klein model or the hyperboloid modelinstance ofand has been described by other models0.80text
obtained by considering the two-sheeted hyperboloid qinstance ofand has been described by other models0.80text
the Riemanninstance ofalthough classical results0.80text
the Gaussinstance ofthere are important global aspects0.80text
Differential geometry of surfacesrelated to External linksWiktionary-logo-en-v20.60section
Differential geometry of surfacesrelated to External linksMedia0.60section
Differential geometry of surfacesrelated to External linksDifferential0.60section

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    Min side: 3
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