| Computational Mathematics |
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| Projectively flat Asanov Finsler metric |
| HAN Jing-wei, YU Yao-yong |
| Department of Mathematics, Zhejiang University, Hangzhou 310027, China; School of Science, Hangzhou Dianzi University, Hangzhou 310028, China |
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Abstract In this work, we study the Asanov Finsler metric F=α(β2/α2+gβ/α+1)1/2exp{(G/2)arctan[β/(hα)+G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(−2,2), h=(1−g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.
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Received: 17 July 2006
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