Deformed Infinite series metric in Cartan Spaces

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 ${}^{\prime }invariant{s}^{\prime }$. In the present paper we determine the ${}^{\prime }invariant{s}^{\prime }$ in two different cases of deformed infinite series metric which characterize the special classes of Cartan spaces ${\ell }^n$.