Geodesic orbit Riemannian spaces with two isotropy summands. I

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 / Hg) with two irreducible submodules in the isotropy representation.

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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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Correspondence to Yuriĭ Nikonorov.

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Chen, Z., Nikonorov, Y. Geodesic orbit Riemannian spaces with two isotropy summands. I. Geom Dedicata 203, 163–178 (2019). https://doi.org/10.1007/s10711-019-00432-6

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Keywords

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

Mathematics Subject Classification (2010)

  • 53C20
  • 53C25
  • 53C35