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I am trying t solution Navier-Stokes equation and I cannot find something about Laplacian. I would like to solution Laplace’a equation for each component.I am trying to transform cylindrical coordinate. I would like to search equation for covariant derivative. For divergence of a contravariant tensor I found:

Aj;k=1/gkk(dAj/dxk)-ri;jkAi

where r is christoffel symbol

I do not know what I have to change that obtain the same for Laplace’a equation? If Christoffel symbols do not change?

I will be grateful for any directions and instructions.