# Christoffel symbols examples

i'm having a hard time computing these so could people show me several examples to help me get a better feel for them before I move on to curvature?

Related Differential Geometry News on Phys.org
cristo
Staff Emeritus
One of the simplest examples would be to calculate the connection coefficients for the 3D Euclidean space using spherical polar coordinates. Here the line element is of the form $$ds^2=dr^2+r^2d\theta^2+r^2\sin^2\theta d\phi^2$$. Could you try this one?

As an aside, have you studied and Lagrangian mechanics? If so, there is a method of obtaining the connection coefficients from the Euler-Lagrange equations which is sometimes less time consuming than using the definition involving the metric tensor.

No but i know the euler lagrage equation.

cristo
Staff Emeritus
Maybe it's easier to just use the definition of the symbols. Try plugging in the metric coefficients and see what you get for the gammas.

Yes but could you still show me some examples, i'm not particularly comfortable with thses symbols.

robphy