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Keywords:
almost Hermitian homogeneous spaces; Singer invariant
almost Hermitian homogeneous spaces; Singer invariant
Summary:
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.
References:
[Ki] Kiričenko V.: On homogeneous Riemannian spaces with invariant tensor structure. Soviet Math. Dokl. 21 (2) (1980), 734-737.
[K1] Kowalski O.: Generalized Symmetric Spaces. Lecture Notes in Math. 805 Springer Berlin (1980). MR 0579184 | Zbl 0431.53042
[K2] Kowalski O.: Counter-example to the ``Second Singer's Theorem''. Ann. Global Anal. Geom. 8 (1990), 211-214. MR 1088512 | Zbl 0736.53047
[KT] Kowalski O., Tricerri F.: A canonical connection for locally homogeneous Riemannian manifolds. D. Ferus et al. Proc. Conf. Global Diff. Geom. and Global Analysis, Berlin, 1990, Lecture Notes in Math. 1481 Springer Berlin (1990), 97-103. MR 1178522
[LT] Lastaria F., Tricerri F.: Curvature orbits and locally homogeneous Riemannian manifolds. Ann. Mat. Pura Appl. 165 (1993), 121-131. MR 1271415 | Zbl 0804.53072
[No] Nomizu K.: Invariant affine connections on homogeneous spaces. Amer. J. Math. 76 (1954), 33-65. MR 0059050 | Zbl 0059.15805
[NT] Nicolodi L., Tricerri F.: On two theorems of I.M. Singer about homogeneous spaces. Ann. Global Anal. Geom. 8 (1990), 193-209. MR 1088511 | Zbl 0676.53058
[Se] Sekigawa K.: Notes on homogeneous almost Hermitian manifolds. Hokkaido Math. J. 7 (1978), 206-213. MR 0509406 | Zbl 0388.53014
[Si] Singer I.M.: Infinitesimally homogeneous spaces. Comm. Pure Appl. Math. 13 (1960), 685-697. MR 0131248 | Zbl 0171.42503
[Tr] Tricerri F.: Locally homogeneous Riemannian manifolds. Rend. Sem. Mat. Univ. Politec. Torino 50/4 (1993), 411-426. MR 1261452 | Zbl 0804.53072
[TV] Tricerri F., Vanhecke L.: Homogeneous Structures on Riemannian Manifolds. London Mathematical Society Lecture Notes Series 83, Cambridge University Press Cambridge (1983). MR 0712664 | Zbl 0509.53043
[TW] Tricerri F., Watanabe Y.: Infinitesimal models and locally homogeneous almost Hermitian manifolds. Math. J. Toyama Univ. 18 (1995), 147-154. MR 1369702 | Zbl 0865.53042
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