$\mathbb{R}$-complex Finsler spaces with infinite series $(\alpha, \beta)$-metric

TL;DR

This paper introduces a new class of $ ext{R}$-complex Finsler spaces with an infinite series $( ext{α,β})$-metric, analyzing their fundamental metric tensors and properties.

Contribution

It defines $ ext{R}$-complex Finsler spaces with a novel infinite series $( ext{α,β})$-metric and derives their fundamental metric tensors and properties.

Findings

Derived explicit forms of metric tensors $g_{ij}$ and $g_{iar{j}}$.

Analyzed properties of the newly defined $ ext{R}$-complex Finsler spaces.

Established foundational aspects of spaces with the specific infinite series $( ext{α,β})$-metric.

Abstract

In the present paper, the notion of $\mathbb{R}$-complex Finsler space with Infinite Series ($\alpha, \beta$)- metric $\dfrac{\beta^2}{\beta - \alpha}$ is defined. The Fundamental metric fields $g_{ij}$, $g_{i\bar{j}}$, their determinants and the inverse of these tensor fields are obtained. Also some properties of these spaces are studied.