Hermitian Manifolds with Flat Associated Connection
Differential Geometry
2011-09-15 v2
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 Kaehler manifolds as well as Hermitian surfaces with vanishing associated conformal curvature tensor are characterized as locally conformal to a Kaehler manifold of constant holomorphic sectional curvatures.
Cite
@article{arxiv.1108.5336,
title = {Hermitian Manifolds with Flat Associated Connection},
author = {Georgi Ganchev and Ognian Kassabov},
journal= {arXiv preprint arXiv:1108.5336},
year = {2011}
}
Comments
This paper has been withdrawn by the authors because of an involuntary violation of the copyright agreement of Kodai Math. Journal