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AIMS Mathematics

2023, Volume 8, Issue 10: 23062-23086. doi: 10.3934/math.20231174
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Research article

New Einstein-Randers metrics on certain homogeneous manifolds arising from the generalized Wallach spaces

  • School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
  • Received: 08 June 2023 Revised: 02 July 2023 Accepted: 05 July 2023 Published: 20 July 2023

  • MSC : 53C25, 53C30

  • In this article, we find several new non-Riemannian Einstein-Randers metrics on some homogeneous manifolds arising from the generalized Wallach spaces. We first prove the existence of Riemannian Einstein metrics on these homogeneous manifolds. Based on these metrics, we prove that there exist non-Riemannian Einstein-Randers metrics on these homogeneous manifolds.

    Citation: Xiaosheng Li. New Einstein-Randers metrics on certain homogeneous manifolds arising from the generalized Wallach spaces[J]. AIMS Mathematics, 2023, 8(10): 23062-23086. doi: 10.3934/math.20231174

    Related Papers:

  • In this article, we find several new non-Riemannian Einstein-Randers metrics on some homogeneous manifolds arising from the generalized Wallach spaces. We first prove the existence of Riemannian Einstein metrics on these homogeneous manifolds. Based on these metrics, we prove that there exist non-Riemannian Einstein-Randers metrics on these homogeneous manifolds.


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    [1] A. Arvanitoyeorgos, K. Mori, Y. Sakane, Einstein metrics on compact Lie groups which are not naturally reductive, Geom. Dedicata, 160 (2012), 261–285. https://doi.org/10.1007/s10711-011-9681-1 doi: 10.1007/s10711-011-9681-1
    [2] D. Bao, C. Robles, Ricci and flag curvatures in Finsler geometry, Cambridge: Cambridge University Press, 2004.
    [3] D. Bao, C. Robles, Z. Shen, Zermelo navigation on Riemannian manifolds, J. Differential Geom., 66 (2004), 377–435. https://doi.org/10.4310/jdg/1098137838 doi: 10.4310/jdg/1098137838
    [4] H. Chen, Z. Chen, S. Deng, New non-naturally reductive Einstein metrics on exceptional simple Lie groups, J. Geom. Phys., 124 (2018), 268–285. https://doi.org/10.1016/j.geomphys.2017.09.011 doi: 10.1016/j.geomphys.2017.09.011
    [5] Z. Chen, S. Deng, K. Liang, Einstein-Randers metrics on some homogeneous manifolds, Nonlinear Anal. Theor., 91 (2013), 114–120. http://doi.org/10.1016/j.na.2013.06.014 doi: 10.1016/j.na.2013.06.014
    [6] Z. Chen, S. Deng, K. Liang, Homogeneous manifolds admitting non-Riemannian Einstein-Randers metrics, Sci. China Math., 58 (2015), 1473–1482. https://doi.org/10.1007/s11425-014-4932-x doi: 10.1007/s11425-014-4932-x
    [7] Z. Chen, Y. Kang, K. Liang, Invariant Einstein metrics on three-locally-symmetric spaces, Commun. Anal. Geom., 24 (2016), 769–792. https://doi.org/10.1007/s00031-009-9052-2. doi: 10.1007/s00031-009-9052-2
    [8] S. Deng, Z. Hou, Homogeneous Einstein-Randers spaces of negative Ricci curvature, C. R. Acad. Sci. Paris, Ser. Ⅰ, 347 (2009), 1169–1172. https://doi.org/10.1016/j.crma.2009.08.006 doi: 10.1016/j.crma.2009.08.006
    [9] Y. Kang, Z. Chen, Einstein Riemannian metrics and Einstein-Randers metrics on a class of homogeneous manifolds, Nonlinear Anal. Theor., 107 (2014), 86–91. https://doi.org/10.1016/j.na.2014.05.003 doi: 10.1016/j.na.2014.05.003
    [10] X. Liu, S. Deng, Homogeneous Einstein-Randers metrics on Aloff-Wallach spaces, J. Geom. Phys., 98 (2015), 196–200. https://doi.org/10.1016/j.geomphys.2015.08.009 doi: 10.1016/j.geomphys.2015.08.009
    [11] B. Najafi, A. Tayebi, A family of Einstein Randers metrics, Int. J. Geom. Methods M., 8 (2011), 1021–1029. https://doi.org/10.1142/s021988781100552x doi: 10.1142/s021988781100552x
    [12] Y. G. Nikonorov, Classification of generalized Wallach space, Geom. Dedicata, 181 (2016), 193–212. https://doi.org/10.1007/s10711-015-0119-z doi: 10.1007/s10711-015-0119-z
    [13] J. S. Park, Y. Sakane, Invariant Einstein metrics on certain homogeneous spaces, Tokyo J. Math., 20 (1997), 51–61.
    [14] H. Wang, S. Deng, Some Einstein-Randers metrics on homogeneous spaces, Nonlinear Anal. Theor., 72 (2010), 4407–4414. https://doi.org/10.1016/j.na.2010.02.015 doi: 10.1016/j.na.2010.02.015
    [15] H. Wang, S. Deng, Left invariant Einstein-Randers metrics on compact Lie groups, Can. Math. Bull., 55 (2012), 870–881. https://doi.org/10.4153/CMB-2011-145-6 doi: 10.4153/CMB-2011-145-6
    [16] H. Wang, S. Deng, Invariant Einstein-Randers metrics on Stiefel manifolds, Nonlinear Anal. Real, 14 (2013), 594–600. https://doi.org/10.1016/j.nonrwa.2012.07.019 doi: 10.1016/j.nonrwa.2012.07.019
    [17] H. Wang, L. Huang, S. Deng, Homogeneous Einstein-Randers metrics on spheres, Nonlinear Anal. Theor., 74 (2011), 6295–6301. https://doi.org/10.1016/j.na.2011.06.008 doi: 10.1016/j.na.2011.06.008
    [18] Z. Yan, S. Deng, On homogeneous Einstein $(\alpha, \beta)$-metrics, J. Geom. Phys., 103 (2016), 20–36. https://doi.org/10.1016/j.geomphys.2015.12.008 doi: 10.1016/j.geomphys.2015.12.008
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  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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