Habibi, Parastoo; Razavi, Asadollah On generalized symmetric Berwald spaces. (English) Zbl 1197.53096 Int. J. Contemp. Math. Sci. 5, No. 13-16, 667-673 (2010). A connected Riemannian manifold \((M, g)\) is said to be generalized symmetric if, at each point \(x\) of \(M\), there is an isometry \(s_x\) of \((M,g)\) with \(x\) as an isolated fixed point. The family \(\{s_x\mid x\in M\}\) is called an s-structure on \((M,g)\). In this paper, the authors generalize this notion to Berwald spaces and study some fundamental properties of such spaces. They prove that each parallel s-structure on a Berwald space must be regular and that any generalized symmetric Berwald surface must be symmetric. Reviewer: Shaoqiang Deng (Tianjin) MSC: 53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics) 53C35 Differential geometry of symmetric spaces Keywords:homogeneous Finsler space; symmetric space; generalized symmetric space; Berwald space PDFBibTeX XMLCite \textit{P. Habibi} and \textit{A. Razavi}, Int. J. Contemp. Math. Sci. 5, No. 13--16, 667--673 (2010; Zbl 1197.53096) Full Text: Link