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.
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Acknowledgements
I would like to thank Christian Yankov who checked the curvature computation in Example 1 by a computer programme and Kamran Shakoor who checked Example 2.
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The author is partially supported by the National Science Fund, Ministry of Education and Science of Bulgaria, under contract DN 12/2.
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Davidov, J. Harmonic Hermitian Structures on Riemannian Manifolds with Skew Torsion. Mediterr. J. Math. 19, 107 (2022). https://doi.org/10.1007/s00009-021-01932-0
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DOI: https://doi.org/10.1007/s00009-021-01932-0