A new class of projectively flat Finsler metrics with constant flag curvatureK=1

Abstract

Available online xxxx Communicated by Z. Shen MSC: 53C60 53C25 Keywords: Flag curvature Projectively flat metric Locally dually flat metricIn this paper, we consider a class of Finsler metrics which obtained by Kropina change of the class of generalized m-th root Finsler metrics. We classify projectively flat Finsler metrics in this class of metrics. Then under a condition, we show that every projectively flat Finsler metric in this class with constant flag curvature is locally Minkowskian. Finally, we find necessary and sufficient condition under which this class of metrics be locally dually flat.

On generalized Kropina change of $m$th root Finsler metrics with special curvature properties

“…Xu and Li [17] studied a class of Finsler metrics called special generalized fourth root metrics and established a necessary and sufficient condition for this Finsler metrics to be projectively flat with constant flag curvature K = 1 . Recently Tayebi and Shahbazi Nia [14] considered a new class of Finsler metrics, namely Kropina change of generalized m th root metrics, and classified such metrics, which are projectively flat and dually flat.…”

Classification of Randers metric of isotropic projective Ricci curvature

“…The Ricci curvature is the result of the Riemann curvature and is defined as follows Ric(x, y) = R i i (x, y). By definition, the Ricci curvature is a positive definite function of degree 2 on y [3].…”

On isotropic projective Ricci curvature of C-reducible Finsler metrics

“…When F (x, y) = √ a ij (x)y i y j is a Riemannian metric, R i k = R i jkl (x)y j y l , where R i jkl (x) denotes the coefficients of the usual Riemannian curvature tensor. Thus, the quantity R y in Finsler geometry is still called the Riemann curvature [20]. The Ricci curvature Ric is defined by Ric := R i i .…”