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On $m$-th root metrics of isotropic projective Ricci curvature | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 3، دوره 4، شماره 2، 2023، صفحه 123-128 اصل مقاله (408.43 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21830.1113 | ||
| نویسندگان | ||
| Mehran Gabrani1؛ Bahman Rezaei* 1؛ Esra Sengelen Sevim2 | ||
| 1Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran | ||
| 2Department of Mathematics, Istanbul Bilgi University, 34060, Eski Silahtaraga Elektrik Santrali, Kazim Karabekir Cad. No: 2/13 Eyupsultan, Istanbul, Turkey | ||
| چکیده | ||
| The Ricci curvature is introduced by spray on $M^n$. Sprays are deformed to projective sprays with a volume form $dV$ on $M^n$. The projective Ricci curvature is defined as the expression of Ricci curvature with sprays. With this paper, we use the new notion that is called weakly isotropic projective Ricci curvature. We have introduced the idea of weakly isotropic projective Ricci curvature in \cite{GRS21Square}. Then we study and characterize $m$-th root metrics of weakly isotropic projective Ricci curvature. We obtain that every $m$-th root metric of weakly isotropic projective Ricci curvature is projectively Ricci-flat. | ||
| کلیدواژه‌ها | ||
| Isotropic projective Ricci curvature؛ Finsler metric؛ m-th root metric | ||
| مراجع | ||
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[1] X. Cheng and B. Rezaei, Erratum and addendum to the paper: “On a class of projective Ricci flat Finsler metrics” [ MR3611783], Publ. Math. Debrecen, 93 (2018), pp. 157–162.
[2] X. Cheng and Z. Shen, Randers metrics of scalar flag curvature, J. Aust. Math. Soc., 87 (2009), pp. 359–370.
[3] M. Gabrani, B. Rezaei, and E. S. Sevim, Square metrics of isotropic projective Ricci curvature. preprint.
[4] M. Gabrani, B. Rezaei, and E. S. Sevim, General spherically symmetric Finsler metrics with constant Ricci and flag curvature, Differential Geom. Appl., 76 (2021), pp. Paper No. 101754, 19.
[5] , On Landsberg warped product metrics, Zh. Mat. Fiz. Anal. Geom., 17 (2021), pp. 468–483.
[6] , On projective invariants of general spherically symmetric finsler spaces in R n, Diff. Geom. Appl., 82 (2022), p. 101869.
[7] M. Gabrani, E. S. Sevim, and Z. Shen, Some projectively ricci-flat (α, β)-metrics, Period. Math. Hung., (2022), pp. 1–16.
[8] L. Ghasemnezhad, B. Rezaei, and M. Gabrani, On isotropic projective Ricci curvature of C-reducible Finsler metrics, Turkish J. Math., 43 (2019), pp. 1730–1741.
[9] T. R. Khoshdani and N. Abazari, Characterization of weakly Berwald fourth root metrics, Ukra¨ın. Mat. Zh., 71 (2019), pp. 976–995.
[10] B.-D. Kim and H.-Y. Park, The m-th root Finsler metrics admitting (α, β)-types, Bull. Korean Math. Soc., 41 (2004), pp. 45–52.
[11] M. Matsumoto and S. Numata, On Finsler spaces with a cubic metric, Tensor (N.S.), 33 (1979), pp. 153– 162.
[12] M. Matsumoto and H. Shimada, On Finsler spaces with 1-form metric. II. Berwald-Mo´or’s metric L = (y 1y 2· y n) 1/n, Tensor (N.S.), 32 (1978), pp. 275–278.
[13] D. G. Pavlov, Four-dimensional time, Space-Time Structure. Algebra and Geometry, (2004), pp. 45–55.
[14] Z. Shen, Differential geometry of spray and Finsler spaces, Kluwer Academic Publishers, Dordrecht, 2001. [15] Z. Shen and L. Sun, On the projective Ricci curvature, Sci. China Math., 64 (2021), pp. 1629–1636.
[16] H. Shimada, On Finsler spaces with the metric L = mp ai1i2...im(x)y i1 y i2 . . . yim, Tensor (N.S.), 33 (1979), pp. 365–372.
[17] A. Tayebi, On 4-th root metrics of isotropic scalar curvature, Math. Slovaca, 70 (2020), pp. 161–172.
[18] A. Tayebi and M. Razgordani, On conformally flat fourth root (α, β)-metrics, Differential Geom. Appl., 62 (2019), pp. 253–266.
[19] A. Tayebi, M. Razgordani, and B. Najafi, On conformally flat cubic (α,β )-metrics, Vietnam J. Math., 49 (2021), pp. 987–1000.
[20] Y. Yu and Y. You, On Einstein m-th root metrics, Differential Geom. Appl., 28 (2010), pp. 290–294. | ||
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