Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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INTRINSIC THEORY OF Cv-REDUCIBILITY IN FINSLER GEOMETRY

  • Salah Gomaa Elgendi (Department of Mathematics Faculty of Science Islamic University of Madinah) ;
  • Amr Soleiman (Department of Mathematics College of Science and Arts - Qurayyat Al Jouf University, Department of Mathematics Faculty of Science Benha University)
  • Received : 2023.04.19
  • Accepted : 2023.11.14
  • Published : 2024.01.31
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Abstract

In the present paper, following the pullback approach to Finsler geometry, we study intrinsically the Cv-reducible and generalized Cv-reducible Finsler spaces. Precisely, we introduce a coordinate-free formulation of these manifolds. Then, we prove that a Finsler manifold is Cv-reducible if and only if it is C-reducible and satisfies the 𝕋-condition. We study the generalized Cv-reducible Finsler manifold with a scalar π-form 𝔸. We show that a Finsler manifold (M, L) is generalized Cv-reducible with 𝔸 if and only if it is C-reducible and 𝕋 = 𝔸. Moreover, we prove that a Landsberg generalized Cv-reducible Finsler manifold with a scalar π-form 𝔸 is Berwaldian. Finally, we consider a special Cv-reducible Finsler manifold and conclude that a Finsler manifold is a special Cv-reducible if and only if it is special semi-C-reducible with vanishing 𝕋-tensor.

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References

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