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On projectively PR-flat Douglas sprays | ||
| Journal of Finsler Geometry and its Applications | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 اسفند 1403 اصل مقاله (313.03 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2025.16385.1143 | ||
| نویسندگان | ||
| Samaneh Jalili؛ Bahman Rezaei* ؛ Mehran Gabrani | ||
| Department of mathematics, Urmia University, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Sprays؛ projective Riemann curvature؛ Douglas curvature | ||
| مراجع | ||
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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. | ||
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آمار تعداد مشاهده مقاله: 33 تعداد دریافت فایل اصل مقاله: 39 |
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