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Geodesic orbit Riemannian spaces with two isotropy summands. I

  • Zhiqi Chen
  • Yuriĭ NikonorovEmail author
Original Paper
First Online:

Abstract

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. The main result is the classification of compact simply connected geodesic orbit Riemannian spaces (G / H, g) with two irreducible submodules in the isotropy representation.

Keywords

Homogeneous Riemannian manifolds Geodesic orbit spaces Normal homogeneous spaces Naturally reductive spaces Weakly symmetric spaces 

Mathematics Subject Classification (2010)

53C20 53C25 53C35 
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Notes

Acknowledgements

The authors are indebted to Prof. Megan Kerr for helpful discussions concerning this paper. The work is partially supported by Grant 1452/GF4 of Ministry of Education and Sciences of the Republic of Kazakhstan for 2015–2017 and NSF of China (No. 11571182).

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinChina
  2. 2.Southern Mathematical Institute of Vladikavkaz Scientific Centre of the Russian Academy of SciencesVladikavkazRussia

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