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Keywords:
naturally reductive spaces; Riemannian g.o. spaces; geodesic graph
naturally reductive spaces; Riemannian g.o. spaces; geodesic graph
Summary:
In ( Dušek, Z., Kowalski, O. and Nikčević, S. Ž., New examples of Riemannian g.o. manifolds in dimension 7, Differential Geom. Appl. 21 (2004), 65–78.), the present authors and S. Nikčević constructed the 2-parameter family of invariant Riemannian metrics on the homogeneous manifolds $M=[{\rm SO}(5)\times {\rm SO}(2)]/{\rm U}(2)$ and $M=[{\rm SO}(4,1)\times {\rm SO}(2)]/{\rm U}(2)$. They proved that, for the open dense subset of this family, the corresponding Riemannian manifolds are g.o. manifolds which are not naturally reductive. Now we are going to investigate the remaining metrics (in the compact case).
References:
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