Para-tt*-bundles on the tangent bundle of an almost para-complex manifold

@article{Schfer2007ParattbundlesOT,
  title={Para-tt*-bundles on the tangent bundle of an almost para-complex manifold},
  author={Lars Christoph Sch{\"a}fer},
  journal={Annals of Global Analysis and Geometry},
  year={2007},
  volume={32},
  pages={125-145}
}
In this paper we study para-tt*-bundles (TM, D, S) on the tangent bundle of an almost para-complex manifold (M, τ). We characterise those para-tt*-bundles with $${\nabla=D + S}$$ induced by the one-parameter family of connections given by $${\nabla^{\theta}=\exp(\theta \tau) \circ \nabla \circ\exp(-\theta \tau)}$$ and prove a uniqueness result for solutions with a para-complex connection D. Flat nearly para-Kähler manifolds and special para-complex manifolds are shown to be such solutions. We… CONTINUE READING