Strong Kaehler with torsion structures from almost contact manifolds

Marisa Fernandez; Anna Fino; Luis Ugarte; Raquel Villacampa

Strong Kaehler with torsion structures from almost contact manifolds

Differential Geometry 2010-11-19 v3

Authors: Marisa Fernandez , Anna Fino , Luis Ugarte , Raquel Villacampa

Abstract

For an almost contact metric manifold $N$ , we find conditions for which either the total space of an $S^1$ -bundle over $N$ or the Riemannian cone over $N$ admits a strong K\"ahler with torsion (SKT) structure. In this way we construct new 6-dimensional SKT manifolds. Moreover, we study the geometric structure induced on a hypersurface of an SKT manifold, and use such structures to construct new SKT manifolds via appropriate evolution equations. Hyper-K\"ahler with torsion (HKT) structures on the total space of an $S^1$ -bundle over manifolds with three almost contact structures are also studied.

Keywords

strong Kähler with torsion SKT structure almost contact metric manifold S^1-bundle Riemannian cone hypersurface hyper-Kähler with torsion HKT structure

Cite

@article{arxiv.0909.3946,
  title  = {Strong Kaehler with torsion structures from almost contact manifolds},
  author = {Marisa Fernandez and Anna Fino and Luis Ugarte and Raquel Villacampa},
  journal= {arXiv preprint arXiv:0909.3946},
  year   = {2010}
}

Comments

23 pages, to appear in Pacific Journal of Mathematics; Section 7 has been modified

Strong Kaehler with torsion structures from almost contact manifolds

Abstract

Keywords

Cite

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