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Finsler Warped Product Metrics with Relatively Isotropic Landsberg Curvature

Published online by Cambridge University Press:  12 May 2020

Zhao Yang
Affiliation:
College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang Province, 830046, China e-mail: [email protected]
Xiaoling Zhang*
Affiliation:
College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang Province, 830046, China e-mail: [email protected]

Abstract

In this paper, we study Finsler warped product metrics with relatively isotropic Landsberg curvature. We obtain the differential equations that characterize such metrics. Then we give some examples.

Type
Article
Copyright
© Canadian Mathematical Society 2020

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Footnotes

This work was supported by National Natural Science Foundation of China (No.11961061, 11461064,11761069).

References

Bishop, R. L. and O’Neill, B., Manifolds of negative curvature. Trans. Amer. Math. Soc. 145(1969), 149.CrossRefGoogle Scholar
Chen, B., Shen, Z., and Zhao, L., Constructions of Einstein Finsler metrics by warped product. Internat. J. Math. 47(2018), 127128. https://doi.org/10.1142/S0129167X18500817Google Scholar
Chen, Y. and Song, W., Spherically symmetric Finsler metrics with isotropic E-curvature. J. Math. Res. Appl. 35(2015), 561567.Google Scholar
Chen, Y. and Song, W., Spherically symmetric Finsler metrics with relatively isotropic Landsberg curvature. Adv. Math. 47(2018), 117128. https://doi.org/10.11845/sxjz.2016075bGoogle Scholar
Cheng, X., Mo, X., and Shen, Z., On the flag curvature of Finsler metrics of scalar curvature. J. London Math. Soc. (2) 68(2003), 762780. https://doi.org/10.1112/S0024610703004599CrossRefGoogle Scholar
Cheng, X., Wang, H., and Wang, M.,(α,β)-metrics with relatively isotropic mean Landsberg curvature. Publ. Math. Debrecen 72(2008), 475485.Google Scholar
Guo, E., Liu, H., and Mo, X., On spherically symmetric Finsler metrics with isotropic Berwald curvature. Int. J. Geom. Methods Mod. Phys. 10(2013), 1350054. https://doi.org/10.1142/S0219887813500540CrossRefGoogle Scholar
He, Y. and Zhang, X., On doubly warped product of Hermitian manifolds. [In Chinese]. Acta Math. Sinica (Chin. ser.) 61(2018), 835842.Google Scholar
He, Y. and Zhong, C., On unitary invariant strongly pseudoconvex complex Landsberg metrics. J. Math. Study 49(2016), 1322. https://doi.org/10.4208/jms.v49n1.16.02Google Scholar
Huang, L. and Mo, X., Projectively flat Finsler metrics with orthogonal invariance. Ann. Polon. Math. 107(2013), 259270. https://doi.org/10.4064/ap107-3-3CrossRefGoogle Scholar
Kozma, L., Peter, R. and Varga, C., Warped product of Finsler manifolds. Ann. Univ. Sci. Budapest 44(2001), 157170.Google Scholar
Lansberg, G., Ber die Totalkrmmung. Jahresber. Dtsch. Math. Ver. 16(1907), 3646.Google Scholar
Lansberg, G., Ber die Krmmung in der Variationsrechnung. Math. Ann. 65(1908), 313349.CrossRefGoogle Scholar
Liu, H. and Mo, X., Finsler warped product metrics of Douglas type. Canad. Math. Bull. 62(2019), 119130. https://doi.org/10.4153/cmb-2017-077-0CrossRefGoogle Scholar
Li, B. and Shen, Z., On a class of weak Landsberg metrics. Sci. China Ser. A 50(2007), 573589. https://doi.org/10.1007/s11425-007-0021-8CrossRefGoogle Scholar
Mo, X., Solrzano, N. M., and Tenenblat, K., On spherically symmetric Finsler metrics with vanishing Douglas curvature. Differential Geom. Appl. 31(2013), 746758. https://doi.org/10.1016/j.difgeo.2013.09.002CrossRefGoogle Scholar
Rutz, S. F., Symmetry in Finsler spaces. In: Finsler geometry (Seattle, WA, 1995), Amer. Math. Soc., Providence, RI, 1996, pp. 289300. https://doi.org/10.1090/conm/196/02459CrossRefGoogle Scholar
Shen, Z., Non-Riemannian quantities. In: Differential geometry of spray and Finsler spaces, Kluwer Academic Publishers, Dordrecht, 2001, pp. 7793.CrossRefGoogle Scholar
Zhou, L., The spherically symmetric Finsler metrics with isotropic S-curvature. J. Math. Anal. Appl. 431(2015), 10081021. https://doi.org/10.1016/j.jmaa.2015.05.074CrossRefGoogle Scholar
Zhu, H., On a class of Finsler metrics with relatively isotropic mean Landsberg curvature. Publ. Math. Debrecen 89(2016), 483498. https://doi.org/10.5486/PMD.2016.7467CrossRefGoogle Scholar