The purpose of this paper is to study hom-algebroids, among them left symmetric homalgebroids and symplectic hom-algebroids by providing some characterizations and geometric interpretations. Therefore, we introduce and study para-Kähler hom-Lie algebroids and show various properties and examples including these structures.2010 Mathematics Subject Classification. 17A30, 17D25, 53C15, 53D05. Key words and phrases.Hom-algebroid, left symmetric hom-algebroid, Hom-Lie algebroid, para-Kähler hom-Lie algebroid.
In this paper, we study Randers metrics and find a condition on Ricci tensor of these metrics to be Berwaldian. This generalize Shen's Theorem which says: every R-flat complete Randers metric is locally Minkowskian. Then we find a necessary and sufficient condition on Ricci tensor under which a Randers metric of scalar flag curvature is of zero flag curvature.
In this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a generalized m-th root metric is conformal to a m-th root metric, then both of them reduce to Riemannian metrics.
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