English

Harmonic Hermitian structures on Riemannian manifolds with skew-torsion

Differential Geometry 2021-07-05 v3

Abstract

We find geometric conditions on a four-dimensional Hermitian manifold endowed with a metric connection with totally skew-symmetric torsion under which the complex structure is a harmonic map from the manifold into its twistor space considered with a natural family of Riemannian metrics defined by means of the metric and the given connection on the base manifold.

Keywords

Cite

@article{arxiv.2105.00426,
  title  = {Harmonic Hermitian structures on Riemannian manifolds with skew-torsion},
  author = {Johann Davidov},
  journal= {arXiv preprint arXiv:2105.00426},
  year   = {2021}
}

Comments

an example added; to appear in Mediterr. J. Math. arXiv admin note: text overlap with arXiv:1504.01610