Read the equation
The displayed expression is the standard coordinate formula combining the inverse metric and first metric derivatives, summed over l. For this file’s metric g=I+φxxᵀ, direct differentiation gives Γᵏᵢⱼ=φxₖδᵢⱼ/(1+φ||x||²). The function instead returns one half of φ(δₖᵢxⱼ+δₖⱼxᵢ), so it does not compute the displayed metric’s connection.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| Gamma | Connection coefficients |
| g_inverse | Inverse metric |
| partial | Coordinate derivative |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
}
}
}
return g
}
// ChristoffelSymbols computes Γ^k_ij connection coefficients
// Γ^k_ij = (1/2) g^kl (∂g_li/∂x^j + ∂g_lj/∂x^i - ∂g_ij/∂x^l)
func ChristoffelSymbols(x []float64) [][][]float64 {
n := len(x)
gamma := make([][][]float64, n)
for k := range gamma {
gamma[k] = make([][]float64, n)
for i := range gamma[k] {
gamma[k][i] = make([]float64, n)
for j := range gamma[k][i] {
// Simplified: Γ^k_ij ≈ φ · δ_ki · x_j + φ · δ_kj · x_iExact original notation
Γ^k_ij = (1/2) g^kl (∂g_li/∂x^j + ∂g_lj/∂x^i - ∂g_ij/∂x^l)