Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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DECOMPOSITION FOR CARTAN'S SECOND CURVATURE TENSOR OF DIFFERENT ORDER IN FINSLER SPACES

  • Abdallah, Alaa A. (Department of Mathematics, Faculty of Education, Abyan University, Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University) ;
  • Navlekar, A.A. (Department of Mathematics, Pratishthan Mahavidyalaya, Science College Dr. Babasaheb Ambedkar Marathwada University) ;
  • Ghadle, Kirtiwant P. (Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University) ;
  • Hamoud, Ahmed A. (Department of Mathematics, Taiz University)
  • Received : 2021.12.14
  • Accepted : 2022.01.08
  • Published : 2022.06.08
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Abstract

The Cartan's second curvature tensor Pijkh is a positively homogeneous of degree-1 in yi, where yi represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan's second curvature tensor Pijkh in two spaces, a generalized 𝔅P-recurrent space and generalized 𝔅P-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.

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References

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