Characterization of Finsler Space with Rander’s-Type Exponential-Form Metric

Vinit Kumar Chaubey, Brijesh Kumar Tripathi, Sudhakar Kumar Chaubey and Meraj Ali Khan ()
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Vinit Kumar Chaubey: Department of Mathematics, North-Eastern Hill University, Shillong 793022, India
Brijesh Kumar Tripathi: Department of Mathematics, L. D. College of Engineering, Navrangpura, Ahmedabad 380015, India
Sudhakar Kumar Chaubey: Section of Mathematics, IT Department, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, Oman
Meraj Ali Khan: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia

Mathematics, 2025, vol. 13, issue 7, 1-15

Abstract: This study explores a unique Finsler space with a Rander’s-type exponential metric, G ( α , β ) = ( α + β ) e β ( α + β ) , where α is a Riemannian metric and β is a 1-form. We analyze the conditions under which its hypersurfaces behave like hyperplanes of the first, second, and third kinds. Additionally, we examine the reducibility of the Cartan tensor C for these hypersurfaces, providing insights into their geometric structure.

Keywords: Finslerian hypersurface; exponential ( α , β )-metric; Cartan connection; hyperplane of first, second, and third kind (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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