SpringerIranian Journal of Science and Technology (Sciences)1028-627632420081212PROJECTIVELY RELATED EINSTEIN FINSLER SPACES421429230010.22099/ijsts.2008.2300ENN.SADEGH-ZADEHDepartment of Mathematics and Computer Science of Amir-Kabir University, Tehran, I. R. of IranA.RAZAVIDepartment of Mathematics and Computer Science of Amir-Kabir University, Tehran, I. R. of IranB.REZAEIDepartment of Mathematics and Computer Science of Amir-Kabir University, Tehran, I. R. of IranJournal Article20061210The main objective of this paper is to find the necessary and sufficient condition of a given Finsler<br />metric to be Einstein in order to classify the Einstein Finsler metrics on a compact manifold. The considered<br />Einstein Finsler metric in the study describes all different kinds of Einstein metrics which are pointwise<br />projective to the given one. This study has resulted in the following theorem that needs the proof of three<br />prepositions. Let F be a Finsler metric (n > 2) projectively related to an Einstein non-projectively flat<br />Finsler metric F , then F is Einstein if and only if F = λ F whereλ is a constant. A Schur type lemma is<br />also proved.http://ijsts.shirazu.ac.ir/article_2300_1d2fa8ed46454558cc9c742c54cbf50f.pdf