If connection of interest is Levi-Civita connection one can find a convenient formula for Laplacian of scalar function in terms of partial derivatives with respect to chosen coordinates: .
where \phi is scalar function, |g| is absolute value of determinant of metric (the use of absolute value is necessary in Pseudo Riemmanian case, for example in General Relativity) and g^{\mu \nu} denotes inverse of the metric tensor .