On the projective algebra of some \((\alpha, \beta)\)-metrics of isotropic S-curvature (Q2865236)

Let \(\alpha \) be a Riemannian metric on the manifold \(M\) and \(\beta \) a \(1\)-form. The Finsler fundamental function \(F=\frac{(\alpha +\beta )^2}{\alpha }\) is called square-metric while \(F=\frac{\alpha ^2}{\alpha -\beta }\) is called Matsumoto metric. The main result of this paper, namely Theorem 1.1, establishes a connection between projective (Killing) algebra of a Matsumoto (square) metric of isotropic \(S\)-curvature and the Killing algebra of \(\alpha \). Another important result isNEWLINENEWLINENEWLINETheorem 1.2: Let \(F\) be a Matsumoto (square) metric of isotropic \(S\)-curvature on a manifold of dimension \(n\geq 3\). Then, \(F\) has a maximal projective symmetry (algebra) if and only if \(F\) either it is a Riemannian metric of constant sectional curvature or locally Minkowskian.