Abstract:In this note it is shown that almost Hermitian locally homogeneous manifolds are determined, up to local isometries, by an integer $k_H$, the covariant derivatives of the curvature tensor up to order $k_H+2$ and the covariant derivatives of the complex structure up to the second order calculated at some point. An example of a Hermitian locally homogeneous manifold which is not locally isometric to any Hermitian globally homogeneous manifold is given.
Keywords: almost Hermitian homogeneous spaces, Singer invariant
AMS Subject Classification: 53C30, 53C55