With the growing interest in and ability of using weak lensing studies to
probe the non-Gaussian properties of the matter density field, there is an
increasing need for the study of suitable statistical measures, e.g. shear
three-point statistics. In this paper we establish the relations between the
three-point configuration space shear and convergence statistics, which are an
important missing link between different weak lensing three-point statistics
and provide an alternative way of relating observation and theory. The method
we use also allows us to derive the relations between other two- and
three-point correlation functions. We show the consistency of the relations
obtained with already established results and demonstrate how they can be
evaluated numerically. As a direct application, we use these relations to
formulate the condition for E/B-mode decomposition of lensing three-point
statistics, which is the basis for constructing new three-point statistics
which allow for exact E/B-mode separation. Our work applies also to other
two-dimensional polarization fields such as that of the Cosmic Microwave
Background.Comment: 17 pages, 5 figures, submitted to A&
