%0 Journal Article
%T On Quaternionic 3 CR-Structure and Pseudo-Riemannian Metric
%A Yoshinobu Kamishima
%J Applied Mathematics
%P 114-129
%@ 2152-7393
%D 2018
%I Scientific Research Publishing
%R 10.4236/am.2018.92008
%X
A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz
metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR- structure) on a 4n + 3 -manifold M. This structure produces a conformal
class [g] of a pseudo-Riemannian metric g of type (4n + 3,3) on M กม S3.
Let (PSp(n +1,1), S4n+3) be the geometric model obtained from the projective
boundary of the complete simply connected quaternionic hyperbolic
manifold. We shall prove that M is locally modeled on (PSp(n +1,1), S4n+3)
if and only if (M กม S3 ,[g]) is conformally flat (i.e. the Weyl conformal curvature
tensor vanishes).
%K Conformal Structure
%K Quaternionic <
%K em>
%K CR<
%K /em>
%K -Structure
%K G-Structure
%K Conformally Flat Structure
%K Weyl Tensor
%K Integrability
%K Uniformization
%K Transformation Groups
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=82568