Hermitian and quaternionic Hermitian structures on tangent bundles
Differential Geometry
2011-12-15 v1
Abstract
We review the theory of quaternionic Kahler and hyperkahler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and with its well estabilished canonical complex structure. With an extra almost Hermitian structure on M it is possible to find a quaternionic Hermitian structure on TM, which is quaternionic Kahler if, and only if, D is flat and torsion free. We also review the symplectic nature of TM. Finally a proper S^3-bundle of complex structures is introduced, expanding to TM the well known twistor bundle of M.
Cite
@article{arxiv.math/0703450,
title = {Hermitian and quaternionic Hermitian structures on tangent bundles},
author = {Rui Albuquerque},
journal= {arXiv preprint arXiv:math/0703450},
year = {2011}
}
Comments
18 pages