A prolongation of the conformal-Killing operator on quaternionic-Kahler manifolds
Differential Geometry
2010-12-30 v2
Abstract
A 2-form on a quaternionic-Kahler manifold (M, g) is called compatible (with the quaternionic structure) if it is a section of the direct sum bundle S^2(H) \oplus S^2(E). We construct a connection D on S^2(H) \oplus S^2(E)\oplus TM, which is a prolongation of the conformal-Killing operator acting on compatible 2-forms. We show that D is flat if and only if the quaternionic-Weyl tensor of (M,g) is zero. Consequences of this result are developed. We construct a skew-symmetric multiplication on the space of conformal-Killing 2-forms on (M,g) and we study its properties in connection with the subspace of compatible conformal-Killing 2-forms.
Keywords
Cite
@article{arxiv.0911.3007,
title = {A prolongation of the conformal-Killing operator on quaternionic-Kahler manifolds},
author = {Liana David},
journal= {arXiv preprint arXiv:0911.3007},
year = {2010}
}
Comments
some proofs from the previous version are simplified