Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON GENERALIZED SHEN'S SQUARE METRIC

  • Amr Soleiman (Department of Mathematics, Faculty of Science, Al Jouf University) ;
  • Salah Gomaa Elgendi (Department of Mathematics, Faculty of Science, Islamic University of Madinah)
  • Received : 2024.04.17
  • Accepted : 2024.08.26
  • Published : 2024.09.30
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Abstract

In this paper, following the pullback approach to global Finsler geometry, we investigate a coordinate-free study of Shen square metric in a more general manner. Precisely, for a Finsler metric (M, L) admitting a concurrent π-vector field, we study some geometric objects associated with ${\widetilde{L}}(x, y)={\frac{(L+{\mathfrak{B}}^2)}L}$ in terms of the objects of L, where ${\mathfrak{B}}$ is the associated 1-form. For example, we find the geodesic spray, Barthel connection and Berwald connection of ${\widetilde{L}}(x,y)$. Moreover, we calculate the curvature of the Barthel connection of ${\tilde{L}}$. We characterize the non-degeneracy of the metric tensor of ${\widetilde{L}}(x,y)$.

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References

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