New examples of Riemannian g.o. manifolds in dimension 7 |
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Authors: | Z Du&scaron ek,S.? Nik?evi? |
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Affiliation: | a Department of Algebra and Geometry, Palacky University, Tomkova 40, 707900 Olomouc, Czech Republic b Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague, Czech Republic c Mathematical Institute SANU, Knez Mihailova 35, p.p 367, 11000 Beograd, Serbia and Montenegro |
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Abstract: | A Riemannian g.o. manifold is a homogeneous Riemannian manifold (M,g) on which every geodesic is an orbit of a one-parameter group of isometries. It is known that every simply connected Riemannian g.o. manifold of dimension ?5 is naturally reductive. In dimension 6 there are simply connected Riemannian g.o. manifolds which are in no way naturally reductive, and their full classification is known (including compact examples). In dimension 7, just one new example has been known up to now (namely, a Riemannian nilmanifold constructed by C. Gordon). In the present paper we describe compact irreducible 7-dimensional Riemannian g.o. manifolds (together with their “noncompact duals”) which are in no way naturally reductive. |
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Keywords: | 22E25 53C30 53C35 53C40 |
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