# Surface divergence of an order 2, rank 3 tensor

1. Mar 24, 2009

### jdber1

I have a 3x3 tensor T that represents the tension of a surface. I need to calculate the surface divergence of this tensor. The surface is defined explicitly by the surface parameters u and v, as are the elements of T. I have looked in a few differential geometry texts and I cannot seem to find a definition for the surface divergence of a tensor I can apply. The fact that T is an order 2, rank 3 tensor and that the surface metric tensor is an order 2, rank 2 tensor, leaves me confused on how to apply any of the definitions of divergence I have found (for example here: http://en.wikipedia.org/wiki/Laplace-Beltrami_operator" [Broken], where the divergence of a vector X is defined). Any help is much appreciated!

Last edited by a moderator: May 4, 2017