Abstract
We study conformal vector fields on a Finsler manifold whose metric is defined by a Riemannian metric, a 1-form and its norm. We find PDEs characterizing conformal vector fields. Then we obtain the explicit expressions of conformal vector fields for certain spherically symmetric metrics on Rn.
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References
Bao D, Robles C, Shen Z. Zermolo navigation on Riemann manifolds. J Differential Geom, 2004, 66: 377–435
Huang L, Mo X. On spherically symmetric Finsler metrics of scalar curvature. J Geom Phys, 2012, 62: 2279–2287
Mo X, Zhou L. The curvature of spherically symmetric Finsler metrics in Rn. ArXiv:1202.4543, 2010
Sevim E S, Shen Z, Ulgen S. Spherically symmetric Finsler metrics with constant Ricci and flag curvature. ArXiv:1505.04182, 2013
Shen Z, Xia Q. On conformal vector fields on Randers manifolds. Sci China Math, 2012, 55: 1869–1882
Shen Z, Xia Q. A class of Randers metrics of scalar flag curvature. Int J Math, 2013, 24: 146–155
Shen Z, Xia Q. Conformal vector fields on a locally projectively flat Randers manifold. Publ Math Debrecen, 2014, 84: 463–474
Shen Z, Xing H. On Randers metrics of isotropic S-curvature. Acta Math Sin Engl Ser, 2008, 24: 789–796
Yu C, Zhu H. On a new class of Finsler metrics. Differential Geom Appl, 2011, 29: 244–254
Zhou L. Projective spherically symmetric Finsler metrics with constant flag curvature in Rn. Geom Dedicata, 2012, 158: 353–364
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Shen, Z., Yuan, M. Conformal vector fields on some Finsler manifolds. Sci. China Math. 59, 107–114 (2016). https://doi.org/10.1007/s11425-015-5099-9
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DOI: https://doi.org/10.1007/s11425-015-5099-9