“$\mathbb{R}$-Complex Finsler spaces with generalized Kropina metric
Keywords:
Complex Finsler space, $\mathbb{R} $-complex Finsler space, Fundamental metric tensors.Abstract
The study of $\mathbb{R}$-complex Finsler spaces with an $(\alpha, \beta)$-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 $F = \frac{\alpha^{m+1}}{\beta^m}$. 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.
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