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Special Projectively Flat(α,β)-Metrics

XIANG Chun-huan1,CHENG Xin-yue21.Department of Mathematics and Computer Science,Chongqing University of Arts and Science,Yongchuan Chongqing 402160,China;2.College of Mathematics and Physics,Chongqing Institute of Technology,Chongqing 400050,China  
In this paper,the authors study approximate exponential metric and prove that the second approximate exponential metric F=α+β+β22α+β36α2 is locally projectively flat if and only ifα is projectively flat and β is parallel with respect to α,where α=aijyiyj,β=biyi.And the same result is obtained for the higher order approximate exponential metric.
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