Nonholonomic Frame for a Deformed $(\alpha,\beta )$-metric

Abstract

Recently, in paper [14], we have introduced the following deformed (α, β)-metric:where α = a ij y i y j is a Riemannian metric;1 is a real parameter and a ∈ 1 4 , +∞ is a real positive scalar. The aim of this paper is to find the nonholonomic frame for this important kind of (α, β)-metric and also to investigate the Frobenius norm for the Hessian generated by this kind of metric.