(α, β, γ) – Metric and its Properties

R K Pandey; Neetu Singh

doi:10.56424/jts.v14i01.10611

R K Pandey Department of Mathematics,Babu Banarasi Das University, Dr. Akhlesh Das Nagar, Chinhut, Lucknow, U.P.,226 028, India.
Neetu Singh Department of Mathematics,Babu Banarasi Das University, Dr. Akhlesh Das Nagar, Chinhut, Lucknow, U.P.,226 028, India.

DOI: https://doi.org/10.56424/jts.v14i01.10611

Keywords: Finsler Space with (α, β, γ) – metric; cubic metric; one form metric; angular metric tensor; fundamental tensor and reciprocal tensor.

Abstract

In the present paper, we have introduced the concept of (α, β, γ) – metric and find some important tensors for (α, β, γ) – metric, where α = { aij (x) y^i y^j}^1/2, 1- form β = bi (x) y^i and cubic metric. γ = { aijk (x) y^i y^j y^k}^ 1/3. We have also considerd the hypersurface given the equation b(x) = constant of the Finsler space with the(α, β, γ) – metric given by L= L (α, β, γ).