  This is the original manuscript dated March 9th 1983, typeset by the Editors
for the Proceedings of the Midwest Geometry Conference 2007 held in memory of
Thomas Branson. Stephen Paneitz passed away on September 1st 1983 while
attending a conference in Clausthal and the manuscript was never published. For
more than 20 years these few pages were circulated informally. In November
2004, as a service to the mathematical community, Tom Branson added a scan of
the manuscript to his website. Here we make it available more formally. It is
surely one of the most cited unpublished articles. The differential operator
defined in this article plays a key role in conformal differential geometry in
dimension 4 and is now known as the Paneitz operator.
