On the geometry of conharmonic curvtuar tensor of nearly kahler manifold

Abstract EN

In this paper we investigated the conharmonic curvature tensor of nearly Kahler manifold.

We proved that, any 4-dimensional NK- manifold is conharmonic-parakähler manifold if and only if, it is manifold of zero scalar curvature.

Also, it has been proved that, NK- manifold of dimension greater than four is conharmonic-parakähler manifold if and only if, it is Ricci-flat Kahler manifold.

Finally, we proved that NK- manifold of dimension greater than four is conharmonic flat if and only if, it is locally holomorphically isometric to the complex space supplied with standard Kahler structure.