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On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics
In this paper, we study a class of two-dimensional Finsler metrics defined by
a Riemannian metric and a 1-form . We characterize those
metrics which are Douglasian or locally projectively flat by some equations. In
particular, it shows that the known fact that is always closed for
those metrics in higher dimensions is no longer true in two dimensional case.
Further, we determine the local structures of two-dimensional
-metrics which are Douglassian, and some families of examples
are given for projectively flat classes with being not closed.Comment: 18 page
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