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On a class of locally dually flat (\(\alpha ,\beta \))-metrics. (English) Zbl 1349.53105

Locally dually flat Finsler metrics arise from information geometry. Some progress on locally dually flat Finsler metrics has been made in recent years. In this paper, based on Xia’s and Cheng-Shen’s works [Q. Xia, Differ. Geom. Appl. 29, No. 2, 233–243 (2011; Zbl 1217.53024); X. Cheng and Z. Shen, Isr. J. Math. 169, 317–340 (2009; Zbl 1165.53016)], the authors find some sufficient conditions for which a locally dually flat \((\alpha, \beta)\)-metrics is Berwaldian, Riemannian, or locally Minkowskian.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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