‎On projectively PR-flat Douglas sprays

Document Type : Original Article

Authors

Department of mathematics, Urmia University, Iran

Abstract

Deformation of every spray into a projective spray can be done using a volume form on a manifold. The Riemann curvature of a projective spray is called the projective Riemmann curvature. In this paper, we present a global rigidity result for projectively PR-flat sprays that have vanishing Douglas curvature. Then we study and characterize projectively PR-flat Randers metrics of Douglas curvature‎.

Keywords


 1. X. Cheng, Y. Shen and X. Ma, On a class of projective Ricci flat Finsler metrics, Publ.Math. Debrecen, 90(2017), : 169-180.
2. X. Cheng, B. Rezaei,
Erratum and addendum to the paper. On a class of projective Ricci flat Finsler metrics, Publ. Math. Debrecen, 93(2018), 1-2.
3. S.S. Chern and Z. Shen,
Riemann-Finsler Geometry, Nankai Tracts in Mathematics, Vol.6, World Scientific, 2005.
4. X. Cheng and Z. Shen,
Finsler Geometry: An Approach via Randers Spaces, Springer Science & Business Media, 2013.
5. M. Gabrani, B. Rezaei and A. Tayebi,
On projective Ricci curvature of Matsumoto metrics, Acta. Math. Univ. Comenianae, 90(2021), 111-126.
6. S. Samadi and B. Rezaei,
Projective Ricci curvature of Randers metrics of navigation data point of view, J. Finsler Geom. Appl. 4(2) (2023), 43-50.
7. Z. Shen and L. Sun,
On the projective Ricci curvature. Sci China Math, 2020, 1-8.
8. H. Zhu and R. Li,
On projective Riemann curvature, Differ. Geom. Appl. 82(2022),101883.
9. Z. Shen,
Differential Geometry of Spray and Finsler Spaces, KluwerAcademic Publishers,2001.
10. H. Zhu,
On a class of projectively Ricci-flat Finsler metrics, Differ. Geom. Appl.73(2020), 101680.
11. H. Zhu and H. Zhang,
Projective Ricci flat spherically symmetric Finsler metrics. Internat. J. Math, 29(11)(2018), 1850078.