EXISTENCE OF SOME RICCI-FLAT FINSLER METRICS

Öz

In this paper, we show the existence of some Ricci-flat Finsler metrics defined by a Riemannian metric and 1-form

Anahtar Kelimeler

• (α β)-metrics,Einstein metrics

Kaynakça

1. Citation1 Bao D, Robles C. On Ricci curvature and flag curvature in Finsler geometry. In: “A Sampler of Finsler Geometry” MSRI series, Cambridge University Press, 2004.
2. Citation2 Cheng X, Shen Z, Tian Y. A class of Einstein (α, β)-metrics. Israel J of Math 2012; 192(1): 221-249.
3. Citation3 Cheng X, Tian Y. Ricci-flat Douglas (α, β)-metrics. Differ. Geom. Appl. 2012; 30(1): 20-32.
4. Citation4 Cheng X, Shen Z. Einstein Finsler Metrics and Killing vector fields on Riemannian Manifolds. Science China Mathematics 2016; 1-16.
5. Citation5 Sevim ES, Shen Z, Zhao L. Some Ricci-flat Finsler metrics. Publ. Math. Debrecen 2013; 83(4): 617-623.
6. Citation6 Li B, Shen Y, Shen, Z. On a class of Douglas metrics. Studia Sci. Math. Hungar. 2009; 46(3): 355-365.