# Riemann curvature tensor and nonlinear operator

1. Jun 30, 2009

### Orbb

Hi,

I hope my questions make sense at all:

Is it possible to define a nonlinear Operator such that letting this Operator act on the Christoffel symbols yields the Riemann curvature tensor (so terms proportional to the derivatives of the Christoffel symbols would have to appear, as well as terms quadratic in the Christoffel symbols)? And, if it is possible to define such an operator, is there any way to test wether it is self-adjoint or not? Any hints appreciated!

If this has been postet in the wrong section (rather mathematical question), feel free to move it.

Orbb