Ricci Curvature Tensor and Non-Riemannian Quantities
Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 530-537

Voir la notice de l'article provenant de la source Cambridge University Press

There are several notions of Ricci curvature tensor in Finsler geometry and spray geometry. One of them is defined by the Hessian of the well-known Ricci curvature. In this paper we will introduce a new notion of Ricci curvature tensor and discuss its relationship with the Ricci curvature and some non-Riemannian quantities. Using this Ricci curvature tensor, we shall have a better understanding of these non-Riemannian quantities.
DOI : 10.4153/CMB-2014-063-4
Mots-clés : 53B40, 53C60, Finsler metrics, sprays, Ricci curvature, non-Riemanian quantity
Li, Benling; Shen, Zhongmin. Ricci Curvature Tensor and Non-Riemannian Quantities. Canadian mathematical bulletin, Tome 58 (2015) no. 3, pp. 530-537. doi: 10.4153/CMB-2014-063-4
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[1] [1] Akbar-Zadeh, H., Sur les espaces de Finsler A courbures sectionnelles constantes. Acad. Roy. Belg. Bull. Cl. Sci. (5). 74(1988), no. 10, 271–322. Google Scholar

[2] [2] Bao, D. and Robles, C., On Ricci curvature and flag curvature in Finslergeometry. In: A sampler of Riemann-Finsler geometry, Math. Sci. Res. Inst. Publ., 50, Cambridge University Press, Cambridge, 2004, pp. 197–259. Google Scholar

[3] [3] Li, B. and Shen, Z., Sprays ofisotropic curvature. Math.Publ. Debrecen, to appear. Google Scholar

[4] [4] Mo, X., On the non-Riemannian quantity H of a Finsler metric. Differential Geom. Appl. 27(2009), no. 1. 7-14. Google Scholar | DOI

[5] [5] Najafi, B., Shen, Z., and Tayebi, A., Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties. Geom. Dedicata. 131(2008), 87–97. http://dx.doi.Org/10.1007/s10711 -007-921 8-9 Google Scholar

[6] [6] Shen, Z., Differential geometry of spray and Finsler spaces. Kluwer Academic Publishers, Dordrecht, 2001. Google Scholar

[7] [7] Shen, Z., On some non-Riemannian quantities in Finsler geometry. Canad.Math. Bull. 56(2013), no. 1, 184–193. Google Scholar | DOI

[8] [8] Xia, Q., Some results on the non-Riemannian quantity H of a Finsler metric. Internat. J. Math. 22(2011), no. 7, 925–936. Google Scholar | DOI

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