Locally dually flat Finsler metrics arise from information geometry. In this paper, we study locally dually flat Kropina metrics and find some equations that characterize locally dually flat Kropina metrics and classify those with scalar flag curvature. Finally, we also classify dually flat Kropina metrics with isotropic [Formula: see text]-curvature.
In this paper, we prove that if a 2-( , 4, ) design admits a flag-transitive automorphism group , then is of affine, almost simple type, or product type. Furthermore, we prove that if is product type then is either a 2-(25, 4, 12) design or a 2-(25, 4, 18) design with Soc( ) = 5 × 5 .
In this paper, we prove that the (α, β)-metrics in the form F = (α+β) p / α p−1 (p = 1, 2) are projectively related to a Randers metric F = ᾱ + β on a manifold of dimension n (n ≥ 3) if and only if F is Berwald metric and F is Douglas metric and the corresponding Riemannian metrics α and ᾱ are projectively related.
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