Geodesic
Infinitesimal characterization of almost Hermitian homogeneous spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 713-721.

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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.
Classification : 53C30, 53C55
Keywords: almost Hermitian homogeneous spaces; Singer invariant 
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     title = {Infinitesimal characterization of almost {Hermitian} homogeneous spaces},
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Console, Sergio; Nicolodi, Lorenzo. Infinitesimal characterization of almost Hermitian homogeneous spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 713-721. http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a8/