Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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GEOMETRY OF LOCALLY PROJECTIVELY FLAT FINSLER SPACE WITH CERTAIN (𝛼, 𝛽)-METRIC

  • AJAYKUMAR, ABBANIRAMAKRISHNAPPA (Department of Mathematics, School of Engineering, Presidency University) ;
  • PRADEEP, KUMAR (Department of Mathematics, School of Engineering, Presidency University)
  • Received : 2022.05.14
  • Accepted : 2022.10.09
  • Published : 2023.01.30
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Abstract

In view of solution to the Hilbert fourth problem, the present study engages to investigate the projectively flat special (𝛼, 𝛽)-metric and the generalised first approximate Matsumoto (𝛼, 𝛽)-metric, where 𝛼 is a Riemannian metric and 𝛽 is a differential one-form. Further, we concluded that 𝛼 is locally Projectively flat and have 𝛽 is parallel with respect to 𝛼 for both the metrics. Also, we obtained necessary and sufficient conditions for the aforementioned metrics to be locally projectively flat.

Keywords

Acknowledgement

The authors wish to express their sincere thanks to the reviewers for the valuable suggestions.

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