Abstract
In this paper a special class of Finsler metrics defined by a Riemannian metric and an 1-form is studied. The projectively flat metrics in dimension \(n\ge 3\) are classified by a new class of metric deformations in Riemann geometry. The results show that the projective flatness of such Finsler metrics always arises from that of some Riemannian metric.
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Acknowledgments
I’d like to thank my tutor Professor Xiaohuan Mo for the useful discussions on this topic when I studied in Peking University. I’d like to thank postgraduate student Xiaoyun Tang in Fudan University for helping me to build some fundamental formulas of \(\beta \)-deformations when she studied in South China Normal University. I should also thank the referees for careful reading and many useful comments.
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This research is supported by a NSFC Grant (No. 11401225).
