Geodesic
Infinitesimal characterization of almost Hermitian homogeneous spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 713-721 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     author = {Console, Sergio and Nicolodi, Lorenzo},
     title = {Infinitesimal characterization of almost {Hermitian} homogeneous spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {713--721},
     year = {1999},
     volume = {40},
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     zbl = {1020.53031},
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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/