\(\mathbb{R}\)-Complex Finsler Spaces With Generalized Kropina Metric - Renu,; Kushwaha, Ramdayal Singh (Communications in Mathematics and Applications, 2024)
The study of \(\mathbb{R}\)-complex Finsler spaces with an \((α, β)\)-metric is a fundamental problem in Finsler geometry. In this paper, we introduce the concept of \(\mathbb{R}\)-complex Finsler spaces with a generalized Kropina metric given by \(F = \frac{α^{m+1}}{β^m}\). We derive explicit formulas for the fundamental metric tensor fields \(g_{ij}\) and \(g_{i\bar{j}}\), as well as their determinants and inverse tensor fields for this metric. Additionally, we discuss various properties of non-Hermitian \(\mathbb{R}\)-complex Finsler spaces with the aforementioned metric.