English Dictionary

Christoffel symbol

noun

(differential geometry) 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,

The Christoffel symbol is used in differential geometry to represent the connection coefficients of a metric connection.

意味（1）

(differential geometry) 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