Finsler Warped Product Metrics of Douglas Type
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 119-130

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

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.
DOI : 10.4153/CMB-2017-077-0
Mots-clés : Finsler metric, warped product, Douglas metric, spherically symmetric metric
Liu, Huaifu; Mo, Xiaohuan. Finsler Warped Product Metrics of Douglas Type. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 119-130. doi: 10.4153/CMB-2017-077-0
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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. . Google Scholar | DOI

[2] Asanov, G. S., Finslerian metric functions over the product R × M and their potential applications . Rep. Math. Phys. 41(1998), no. 1, 117–132. . Google Scholar | DOI

[3] Bishop, R. L. and O’Neill, B., Manifolds of negative curvature . Trans. Amer. Math. Soc. 145(1969), 1–49. . Google Scholar | DOI

[4] Chen, B., Shen, Z., and Zhao, L., Constructions of Einstein Finsler metrics by warped product. preprint, 2016. Google Scholar

[5] Chern, S.-S. and Shen, Z., Riemann-Finsler geometry. Nankai Tracts in Mathematics, 6, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. . Google Scholar | DOI

[6] Douglas, J., The general geometry of paths . Ann. of Math. 29(1927–1928), no. 1–4, 143–168. . Google Scholar | DOI

[7] Huang, L. and Mo, X., Projectively flat Finsler metrics with orthogonal invariance . Ann. Polon. Math. 107(2013), no. 3, 259–270. . Google Scholar | DOI

[8] Kozma, L., Peter, R., and Varga, C., Warped product of Finsler manifolds . Ann. Univ. Sci. Budapest 44(2001), 157–170. Google Scholar

[9] Mccarthy, P. J. and Rutz, S. F., The general four-dimensional spherically symmetric Finsler space . Gen. Relativity Gravitation 25(1993), no. 6, 589–602. . Google Scholar | DOI

[10] Mo, X., Solórzano, N. M., and Tenenblat, K., On spherically symmetric Finsler metrics with vanishing Douglas curvature . Differential Geom. Appl. 31(2013), 746–758. . Google Scholar | DOI

[11] Rutz, S. F., Symmetry in Finsler spaces . In: Finsler geometry (Seattle, WA, 1995), Contemp. Math., 196, American Mathematical Society, Providence, RI, 1996, pp. 289–300. . Google Scholar | DOI

[12] Shen, Z., On R-quadratic Finsler spaces . Publ. Math. Debrecen. 58(2001), no. 1–2, 263–274. Google Scholar

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

[14] Zhou, L., Spherically symmetric Finsler metrics in R n . Publ. Math. Debrecen 80(2012), no. 1–2, 67–77. . Google Scholar | DOI

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