%0 Journal Article %A Tayebi, Akbar %A Bahadori, Morad %A Sadeghi, Hassan %T λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants %J Mathematical Researches %V 6 %N 4 %U http://mmr.khu.ac.ir/article-1-2868-en.html %R 10.52547/mmr.6.4.621 %D 2020 %K Projective invariant, Projectively flat metric, Projectively related metrics, Douglas metric, Weyl metric, Generalized Douglas-Weyl metric., %X Introduction In this paper, by using the concept of spherically symmetric Finsler metric, we define the notion of -projectively related metrics as an extension of projectively related metrics. We construct some non-trivial examples of -projectively related metrics. Let F and be two -projectively related metrics on a manifold M. We find the relation between the geodesics of F and and prove that any geodesic of F is a multiple of a geodesic of and the other way around. There are several projective invariants of Finsler metrics, namely, Douglas metrics, Weyl metrics and generalized Douglas-Weyl curvature. We prove that the Douglas metrics, Weyl metrics and generalized Douglas-Weyl metrics are -projective invariants. Material and methods First we obtain the spray coefficients of a spherically symmetric Finsler metric. By considering it, we define -projectively related metrics which is a generalization of projectively related Finsler metrics. Then we find the geodesics of two -projectively related metrics. We obtain the relation between Douglas, Weyl and generalized Douglas-Weyl curvatures of two -projectively related metrics. Results and discussion We find the Douglas curvature, Weyl curvature and generalized Douglas-Weyl curvature of two -projectively related Finsler metrics. These calculations tell us that these class of Finsler metrics are -projective invariants. Conclusion The following conclusions were drawn from this research. We prove that the Douglas curvature, Weyl curvature and generalized Douglas-Weyl curvature are -projective invariants. Let F and be two -projectively related metrics on a manifold M. We show that F is a Berwald metric if and only if is a Berwald metric. ./files/site1/files/64/12.pdf %> http://mmr.khu.ac.ir/article-1-2868-en.pdf %P 621-630 %& 621 %! %9 Original Manuscript %L A-10-679-1 %+ University of Qom %G eng %@ 2588-2546 %[ 2020