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Finsler Warped Product Metrics of Douglas Type

  • Huaifu Liu (a1) and Xiaohuan Mo (a2)

In this paper, we study the warped structures of Finsler metrics. We obtain the differential equation that characterizes Finsler warped product metrics with vanishing Douglas curvature. By solving this equation, we obtain all Finsler warped product Douglas metrics. Some new Douglas Finsler metrics of this type are produced by using known spherically symmetric Douglas metrics.

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This work is supported by BNSF(1164009), Beijing Postdoctoral Research Foundation and the National Natural Science Foundation of China 11371032 and 11771020. The second author (Xiaohuan Mo) is the corresponding author.

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[1] Alipour-Fakhri, Y. and Rezaii, M. M., The warped Sasaki-Matsumoto metric and bundlelike condition . J. Math. Phys. 51(2010), no. 12, 122701, 13 pp.
[2] Asanov, G. S., Finslerian metric functions over the product R × M and their potential applications . Rep. Math. Phys. 41(1998), no. 1, 117132.
[3] Bishop, R. L. and O’Neill, B., Manifolds of negative curvature . Trans. Amer. Math. Soc. 145(1969), 149.
[4] Chen, B., Shen, Z., and Zhao, L., Constructions of Einstein Finsler metrics by warped product. preprint, 2016.
[5] Chern, S.-S. and Shen, Z., Riemann-Finsler geometry. Nankai Tracts in Mathematics, 6, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005.
[6] Douglas, J., The general geometry of paths . Ann. of Math. 29(1927–1928), no. 1–4, 143168.
[7] Huang, L. and Mo, X., Projectively flat Finsler metrics with orthogonal invariance . Ann. Polon. Math. 107(2013), no. 3, 259270.
[8] Kozma, L., Peter, R., and Varga, C., Warped product of Finsler manifolds . Ann. Univ. Sci. Budapest 44(2001), 157170.
[9] McCarthy, P. J. and Rutz, S. F., The general four-dimensional spherically symmetric Finsler space . Gen. Relativity Gravitation 25(1993), no. 6, 589602.
[10] Mo, X., Solórzano, N. M., and Tenenblat, K., On spherically symmetric Finsler metrics with vanishing Douglas curvature . Differential Geom. Appl. 31(2013), 746758.
[11] Rutz, S. F., Symmetry in Finsler spaces . In: Finsler geometry (Seattle, WA, 1995), Contemp. Math., 196, American Mathematical Society, Providence, RI, 1996, pp. 289300.
[12] Shen, Z., On R-quadratic Finsler spaces . Publ. Math. Debrecen. 58(2001), no. 1–2, 263274.
[13] Shen, Z., Differential geometry of spray and Finsler spaces. Kluwer Academic Publishers, Dordrecht, 2001.
[14] Zhou, L., Spherically symmetric Finsler metrics in R n . Publ. Math. Debrecen 80(2012), no. 1–2, 6777.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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