Bukan (County) Education Office, Department of Education, West Azarbaijan, Iran.
10.22034/jdgaa.2025.2052735.1013
چکیده
The theory of m-th root Finsler metrics has been applied to Ecology, Biology, Seismic Ray Theory, Gravitation, etc. It is regarded as a direct generalization of Riemannian metric in a sense, that is, the second root metric is a Riemannian metric. On the other hand, the Riemannian curvature faithfully reveals the local geometric properties of a Riemann-Finsler metric. In this paper, we will study the class of quintic (α, β)-metrics. We show that 3-th root(α, β)-metrics has a unbound Cartan torsion. Also, we focus on the class of 3-th root (α, β)-metrics. We will study the bound Cartan torsion for a 3-th, 4-th and 5-th root (α, β)-metrics.
مجله هندسه دیفرانسیل، کاربردها و جنبهها