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On Finsler warped product metrics with vanishing $E$-curvature | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 2، شماره 2، آذر 2021، صفحه 137-142 اصل مقاله (316.27 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.19817.1052 | ||
| نویسندگان | ||
| Ranadip Gangopadhyay؛ Anjali Shriwastawa؛ Bankteshwar Tiwari* | ||
| DST-CIMS, Banaras Hindu University, Varanasi-221005, India | ||
| چکیده | ||
| In this paper, we study Finsler warped product metric recently introduced by P. Marcal and Z. Shen and find characteristics differential equations for this metric to have vanishing $E$-curvature. We also prove that if this warped product Finsler metric is projectively flat, then it becomes a Riemannian metric. | ||
| کلیدواژهها | ||
| Finsler metrics؛ Warped product؛ $E$-curvature؛ Projectively flat | ||
| مراجع | ||
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[1] R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49.
[2] J. Nash, C 1 -isometric imbeddings, Ann. of Math. 60(3) (1954), 383-396.
[3] J. Nash,The imbedding problem for Riemannian manifolds, Ann. of Math. 63(1) (1956), 20-63.
[4] B. Chen, Z. Shen and L. Zhao ,Constructions of Einstein Finsler Metrics by Warped Product, Internat. J. Math. 29(11) (2018), 1850081.
[5] L. Kozma, R. Peter and C. Varga, Warped product of Finsler manifolds, Ann Univ Sci Budapest. 44 (2001) 157-170.
[6] H. Liu and X. Mo, Finsler warped product metrics of Douglas type, Canad. Math. Bull. 62(1) (2019), 119-130.
[7] R. Gangopadhyay, A. Shriwastawa and B. Tiwari, On equivalence of two non-Riemannian curvatures in warped product Finsler metrics, arXiv:2011.12045 [math.DG].
[8] B. Tiwari, R. Gangopadhyay and G. K. Prajapati, A class of Finsler spaces with general (α, β)-metrics, Int. J. Geom. Methods Mod. Phys. 16(2) (2019), 1950102.
[9] B. Tiwari, R. Gangopadhyay and G. K. Prajapati, On general (α, β)-metrics with some curvature properties, Khayyam J. Math. 5(2) (2019), 30-39.
[10] R. Bryant, Some remarks on Finsler manifolds with constant flag curvature, Houston J. Math. 28(2) (2002), 221-262.
[11] C. Yu and H. Zhu, On a new class of Finsler metrics, Differential Geom. Appl. 29 (2011), 244-254.
[12] X. Mo, N. M. Solorzano and K. Tenenblat, On spherically symmetric Finsler metrics with vanishing Douglas curvature, Differential Geom. Appl. 31 (2013), 746-758.
[13] Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Adv. Math. 128(2) (1997), 306-328.
[14] Z. Shen, Finsler metrics with K = 0 and S = 0, Canadian J. Math. 55 (2003), 112-132.
[15] Z. Shen, Finsler manifolds of constant positive curvature, Contemp. Math. 196 (1995), 83-93.
[16] H. Zhu, On general (α, β)-metrics with isotropic S-curvature, J. Math. Anal. Appl. 464 (2018), 1127-1142.
[17] X. Cheng and Z. Shen, Randers metric with special curvature properties, Osaka J. Math. 40 (2003), 87-101.
[18] S. S. Chern and Z. Shen, Riemannian-Finsler geometry, World Scientific Publisher, Singapore, 2005.
[19] E. Peyghana and A. Tayebi, On doubly warped product Finsler manifolds, Nonlinear Anal. Real World Appl. 13 (2012), 1703-1720.
[20] M. M. Rezaii and Y. Alipour-Fakhri, On projectively related warped product Finsler manifolds, Int. J. Geom. Methods Mod. Phys. 8(5), (2012) 953-967.
[21] P. Marcal and Z.Shen, Ricci flat Finsler metrics by warped product, arXiv:2012.05699v1 [math.DG] 10 Dec 2020.
[22] G. S. Asanov, Finslerian extensions of Schwarzschild metric, Fortschr. Phys. 40 (1992), 667-693.
[23] G. S. Asanov, Finslerian metric functions over the product and their potential applications, Fortschr. Phys. 40 (1992), 667-693. | ||
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