Geodesic
The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.
Keywords: Finsler manifold; Einstein Randers metric; Ricci curvature. 
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Enli Guo; Xiaohuan Mo; Xianqiang Zhang. The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a44/

[1] Bao D., Robles C., “Ricci and flag curvatures in Finsler geometry”, A Sampler of Riemann–Finsler Geometry, Math. Sci. Res. Inst. Publ., 50, Cambridge Univ. Press, Cambridge, 2004, 197–259 | MR | Zbl

[2] Bao D., Robles C., Shen Z., “Zermelo navigation on Riemannian manifolds”, J. Differential Geom., 66 (2004), 377–435 ; math.DG/0311233 | MR | Zbl

[3] Hamel G., “Über die Geometrieen in denen die Geraden die Kürzesten sind”, Math. Ann., 57 (1903), 231–264 | DOI | MR | Zbl

[4] Hawking S. W., “Gravitational Instantons”, Phys. Lett. A, 60 (1977), 81–83 | DOI | MR

[5] LeBrun C., “Complete Ricci-flat Kähler metrics on $C^n$ need not be flat”, Several Complex Variables and Complex Geometry, Part 2 (Santa Cruz, CA, 1989), Proc. Sympos. Pure Math., 52, Amer. Math. Soc., Providence, RI, 1991, 297–304 | MR

[6] Mo X., An introduction to Finsler geometry, Peking University Series in Mathematics, 1, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006 | MR

[7] Pantilie R., “Harmonic morphisms with 1-dimensional fibres on 4-dimensional Einstein manifolds”, Comm. Anal. Geom., 10 (2002), 779–814 | MR | Zbl

[8] Randers G., “On an asymmetric metric in the four-space of general relativity”, Phys. Rev., 59 (1941), 195–199 | DOI | MR

[9] Robles C., Einstein metrics of Randers type, Ph.D. Thesis, British Columbia University, Canada, 2003

[10] Shen Z., “Projectively flat Randers metrics of constant curvature”, Math. Ann., 325 (2003), 19–30 | DOI | MR | Zbl

[11] Wood J. C., “Harmonic morphisms between Riemannian manifolds”, Modern Trends in Geometry and Topology, Cluj Univ. Press, Cluj-Napoca, 2006, 397–414 | MR | Zbl