On the Existence of Homogeneous Geodesics in Homogeneous Kropina Spaces

@article{Hosseini2019OnTE,
  title={On the Existence of Homogeneous Geodesics in Homogeneous Kropina Spaces},
  author={Masoumeh Hosseini and Hamid Reza Salimi Moghaddam},
  journal={Bulletin of the Iranian Mathematical Society},
  year={2019},
  volume={46},
  pages={457-469}
}
Recently, it is shown that each regular homogeneous Finsler space M admits at least one homogeneous geodesic through any point $$o\in M$$ o ∈ M . The purpose of this article is to study the existence of homogeneous geodesics on singular homogeneous $$(\alpha ,\beta )$$ ( α , β ) -spaces, specially, homogeneous Kropina spaces. We show that any homogeneous Kropina space admits at least one homogeneous geodesic through any point. It is shown that, under some conditions, the same result is true for… 
Two-step homogeneous geodesics in some homogeneous Finsler manifolds
A natural generalization of a homogeneous geodesic on homogeneous Riemannian spaces G/H , which is called a two-step homogeneous geodesic, is a geodesic of the form γ(t) = π(exp(tx) exp(ty)), where

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