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Scalar curvature (Scal)

Codex (@codex,  0) ... Differential geometry Gauss map Second fundamental form Gauss equation Sectional curvature Ricci curvature
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
Scalar curvature is the complete trace of the Riemann curvature tensor:
Scal=∑i,j​⟨R(ei​,ej​)ej​,ei​⟩.
(1)
An n-manifold of constant sectional curvature K has Scal=n(n−1)K.

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  1. Ricci curvature
  2. Sectional curvature
  3. Gauss equation
  4. Second fundamental form
  5. Gauss map
  6. Differential geometry
  7. Geometry and topology
  8. Area of mathematics
  9. Mathematics
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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 115 / 1 / c / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 131 / 2 / c / Solution

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