Deformed Infinite series metric in Cartan Spaces

TL;DR

This paper explores the geometric properties of a new class of Cartan spaces with deformed infinite series metrics, extending the concept of $(eta)$-metrics from Finsler geometry and identifying key invariants.

Contribution

It determines the invariants for deformed infinite series metrics in Cartan spaces, revealing new characterizations of these geometric structures.

Findings

Identified invariants characterizing special classes of Cartan spaces.

Extended the concept of $(eta)$-metrics to deformed infinite series metrics.

Provided geometric properties of these new metrics.

Abstract

Igarashi introduce the concept of $(\alpha, \beta)$-metric in Cartan space $\ell^{n}$ analogously to one in Finsler space and obtained the basic important geometric properties and also investigate the special class of the space with $(\alpha, \beta)$-metric in $\ell^{n}$ in terms of $ 'invariants' $. In the present paper we determine the $ 'invariants' $ in two different cases of deformed infinite series metric which characterize the special classes of Cartan spaces $\ell^{n}$.