http://arxiv.org/abs/1411.2283
Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and the generating vector field, and is provided for from two equivalent perspectives: a Lagrangian specification with respect to a generalized parameter, and an Eulerian specification making explicit the evolution dynamics. Furthermore, we provide explicit non-trivial conditions which govern the transformation properties of the referential gradient object.
J. Edmondson
Tue, 11 Nov 14
60/61
Comments: Communications in Mathematical Physics. Submitted 9 Nov 2014