Volume 6, Issue 4 (Vol. 6, No. 4, 2020)                   mmr 2020, 6(4): 621-630 | Back to browse issues page


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Tayebi A, Bahadori M, Sadeghi H. λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants. mmr 2020; 6 (4) :621-630
URL: http://mmr.khu.ac.ir/article-1-2868-en.html
1- University of Qom , akbar.tayebi@gmail.com
2- University of Qom
Abstract:   (2124 Views)
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
 
Full-Text [PDF 568 kb]   (334 Downloads)    
Type of Study: Original Manuscript | Subject: alg
Received: 2018/10/31 | Revised: 2021/02/16 | Accepted: 2019/07/23 | Published: 2021/01/29 | ePublished: 2021/01/29

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