A Paneitz-type operator for CR pluriharmonic functions
Differential Geometry
2013-09-11 v1 Complex Variables
Abstract
We introduce a fourth order CR invariant operator on pluriharmonic functions on a three-dimensional CR manifold, generalizing to the abstract setting the operator discovered by Branson, Fontana and Morpurgo. For a distinguished class of contact forms, all of which have vanishing Hirachi- curvature, these operators determine a new scalar invariant with properties analogous to the usual -curvature. We discuss how these are similar to the (conformal) Paneitz operator and -curvature of a four-manifold, and describe its relation to some problems for three-dimensional CR manifolds.
Cite
@article{arxiv.1309.2528,
title = {A Paneitz-type operator for CR pluriharmonic functions},
author = {Jeffrey S. Case and Paul Yang},
journal= {arXiv preprint arXiv:1309.2528},
year = {2013}
}
Comments
26 pages; to appear in Bull. Inst. Math. Acad. Sin. (N.S.)