Lexic.us

Definition of Christoffel symbol

1. Noun. (context: differential geometry) For a surface with parametrization $\backslash vec\; x\; (u,v)$, and letting $i,\; j,\; k\; \backslash in\; \backslash \{u,\; v\backslash \}$, the Christoffel symbol $\backslash Gamma\_\{i\; j\}^k$ is the component of the second derivative $\backslash vec\; x\_\{i\; j\}$ in the direction of the first derivative $\backslash vec\; x\_k$, and it encodes information about the surface's curvature. Thus, ¹

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