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sectional curvature

scalar quantity; given two unit tangent vectors u, v at the same point, defined as K(u,v) = ⟨R(u,v)v,u⟩/(1-⟨u,v⟩²), where R is the Riemann curvature
Thing Curvature Of Riemannian Manifolds Q855622

Facts

4 properties
Instance of
curvature of Riemannian manifolds, mathematical object[2]
Defining formula
K(u,v)=\frac{\langle R(u,v)v,u\rangle}{\langle u,u\rangle\langle v,v\rangle-\langle u,v\rangle^2}[3]
In defining formula
R, \langle~,~\rangle, K, u, v[5][6][7][8][9]
Maintained by WikiProject
WikiProject Mathematics[4]
🏷️ Also known as
en sectional curvature de Schnittkrümmung fr сourbure sectionnelle it curvatura sezionale ja 断面曲率 ko 단면 곡률 nl sectiekromming ro curbură secțională ru секционная кривизна uk cекційна кривина zh 截面曲率
🔖 Identifiers · 6
OpenAlex ID
C42448751
Freebase ID
/m/01pzql
Lexikon der Mathematik entry ID
8832
MathWorld ID
SectionalCurvature
Microsoft Academic ID (discontinued)
42448751
NLab ID
sectional curvature

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🔗 Connections
Instance of 1
mathematical object
Maintained by WikiProject 1
WikiProject Mathematics
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Summary

sectional curvature is a curvature of Riemannian manifolds[1].

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.
  6. [7] ↑ . wikidata.org.
  7. [8] ↑ . wikidata.org.
  8. [9] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

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