Characterization of weakly Berwald fourth root metrics

Abstract

UDC 514.7
In recent studies, it is shown that the theory of fourth root metrics plays a very important role in physics, theory of space-time structures, gravitation, and general relativity. The class of weakly Berwald metrics contains the class of Berwald metrics as a special case. We establish the necessary and sufficient condition under which the fourth root Finsler space with an $(\alpha, \beta)$-metric is a weakly Berwald space.