Christoffel symbol

noun

For a surface with parametrization ⃑x(u,v), and letting i,j,k∈u,v, the Christoffel symbol Γᵢⱼᵏ is the component of the second derivative ⃑x_ij in the direction of the first derivative ⃑x_k, and it encodes information about the surface's curvature. Thus,

“⃑x_uu\⃑x_uv\⃑x_vv=ΓᵤᵤᵘΓᵤᵤᵛl\ΓᵤᵥᵘΓᵤᵥᵛm\ΓᵥᵥᵘΓᵥᵥᵛn⃑x_u\⃑x_v\⃑n”

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Meanings

nounChristoffel symbol (plural Christoffel symbols)

plural Christoffel symbols

  1. differential geometryFor a surface with parametrization ⃑x(u,v), and letting i,j,k∈u,v, the Christoffel symbol Γᵢⱼᵏ is the component of the second derivative ⃑x_ij in the direction of the first derivative ⃑x_k, and it encodes information about the surface's curvature. Thus,

    ⃑x_uu\⃑x_uv\⃑x_vv=ΓᵤᵤᵘΓᵤᵤᵛl\ΓᵤᵥᵘΓᵤᵥᵛm\ΓᵥᵥᵘΓᵥᵥᵛn⃑x_u\⃑x_v\⃑n

Origin

Named for Elwin Bruno Christoffel (1829–1900).

Full word history & related roots →

Translations

Bulgarian символ на Кристофел
  • символ на Кристофел (simvol na Kristofel)component of second derivative
Cite this entry
APA

Christoffel symbol. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Christoffel%20symbol

MLA

“Christoffel symbol.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Christoffel%20symbol. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Christoffel symbol,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Christoffel%20symbol.

Source: Christoffel symbol on Wiktionary, CC BY-SA 4.0.