• Mathematics
  • Published 2018

On Gauduchon connections with K\"ahler-like curvature

  title={On Gauduchon connections with K\"ahler-like curvature},
  author={Daniele Angella and Antonio Otal and Luis Angel Ugarte and R. Escart{\'i}n Villacampa},
We study Hermitian metrics with a Gauduchon connection being "K\"ahler-like", namely, satisfying the same symmetries for curvature as the Levi Civita and Chern connections. In particular, we investigate $6$-dimensional solvmanifolds with invariant complex structures with trivial canonical bundle and with invariant Hermitian metrics. The results for this case give evidence for two conjectures that are expected to hold in more generality: first, if the Bismut connection is K\"ahler-like, then the… CONTINUE READING
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