Shanker G.Rani S.2020-02-182024-08-132020-02-182024-08-132020219887810.1142/S021988782050019Xhttps://kr.cup.edu.in/handle/32116/2604The study of curvature properties of homogeneous Finsler spaces with (?,?)-metrics is one of the central problems in Riemann-Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for S-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of S-curvature, the mean Berwald curvature of aforesaid (?,?)-metric is calculated.enHomogeneous Finsler spaceinvariant vector fieldmean Berwald curvatureS -curvaturesquare metricArticlehttps://www.worldscientific.com/doi/10.1142/S021988782050019X