- #1
Sajet
- 48
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Hi!
I'm trying to understand the formula for the Laplace-Beltrami Operator on a Riemannian manifold.
(http://en.wikipedia.org/wiki/List_o...vergence.2C_Laplace.E2.80.93Beltrami_operator)
Specifically, how the determinant of the metric tensor comes into play when defining the the Laplace-Beltrami-Operator by trace(Hess f). I have found a computation by Peter Petersen but I don't understand one (probably very simple) step (See attachment).
I would love to know how the determinant disappears in this step.
Thank you in advance
I'm trying to understand the formula for the Laplace-Beltrami Operator on a Riemannian manifold.
(http://en.wikipedia.org/wiki/List_o...vergence.2C_Laplace.E2.80.93Beltrami_operator)
Specifically, how the determinant of the metric tensor comes into play when defining the the Laplace-Beltrami-Operator by trace(Hess f). I have found a computation by Peter Petersen but I don't understand one (probably very simple) step (See attachment).
I would love to know how the determinant disappears in this step.
Thank you in advance