1. Invariant Shen connections and geodesic orbit spaces
- Author
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Muzsnay, Zoltán and Péter T., Nagy
- Abstract
The geodesic graph of Riemannian spaces all geodesics of which are orbits of 1-parameter isometry groups was constructed by J. Szenthe in 1976 and it became a basic tool for studying such spaces, called g.o.\ spaces. This infinitesimal structure corresponds to the reductive complement
]]>\mathfrak m$ in the case of naturally reductive spaces. The systematic study of Riemannian g.o. spaces was started by O. Kowalski and L.~Vanhecke in 1991, when they introduced the most important definitions, classified the low-dimensional examples and described the basic constructions of this theory. The aim of this paper is to investigate a connection theoretical analogue of the concept of the geodesic graph.The geodesic graph of Riemannian spaces all geodesics of which are orbits of 1-parameter isometry groups was constructed by J. Szenthe in 1976 and it became a basic tool for studying such spaces, called g.o.\ spaces. This infinitesimal structure corresponds to the reductive complement ]]>\mathfrak m$ in the case of naturally reductive spaces. The systematic study of Riemannian g.o. spaces was started by O. Kowalski and L.~Vanhecke in 1991, when they introduced the most important definitions, classified the low-dimensional examples and described the basic constructions of this theory. The aim of this paper is to investigate a connection theoretical analogue of the concept of the geodesic graph.- Published
- 2005
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