On sprays of scalar curvature and metrizability (Q2688210)

In the present paper author have considered a new notion for sprays of constant curvature, shows that a spray of isotropic curvature is not necessarily of constant curvature even in dimension \(n\geq 3\). Further, complete conditions are given for sprays of isotropic (resp. constant) curvature to be Finsler metrizable. Based on this result, the local structure is determined for locally projectively flat Berwald sprays of isotropic (resp. constant) curvature which are Finsler metrizable, and some more sprays of isotropic curvature are discussed for their metrizability. Besides, the metrizability problem is also investigated for sprays of scalar curvature under certain curvature conditions.