Papers
Authors
Leo Brewin
Abstract
A detailed analysis of the Riemann tensor in the neighbourhood of one
bone and of the extrinsic curvature in the neighbourhood of one
triangular face in a simplicial geometry is presented. Unlike most
previous analyses this analysis makes no reference to any particular
choice of smoothing scheme. Explicit formulae will be presented for
both the Riemann and extrinsic curvature tensors. These results are
applied, using the formalism developed in an earlier paper [1], in
deriving an exact formula for the integral extrinsic curvature. It is
argued that for integrals of R^2,R^3,... contributions must be
expected from the legs, vertices,... rather than just from the bones.
This work provides the background material for the following paper in
which the Gauss-Codacci equation is applied to a Regge spacetime.
Reference