# \(\mathbb{R}\)-Complex Finsler Spaces With Generalized Kropina Metric

## DOI:

https://doi.org/10.26713/cma.v15i1.2388## 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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*Communications in Mathematics and Applications*,

*15*(1), 243–252. https://doi.org/10.26713/cma.v15i1.2388

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