Abstract
A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally conformal Kähler manifolds as well as Hermitian surfaces with vanishing associated conformal curvature tensor are characterized as locally conformal to a Kähler manifold of constant holomorphic sectional curvatures.
Citation
G. Ganchev. O. Kassabov. "Hermitian manifolds with flat associated connection." Kodai Math. J. 29 (2) 281 - 298, June 2006. https://doi.org/10.2996/kmj/1151936442
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