Research article Special Issues

On gradient normalized Ricci-harmonic solitons in sequential warped products

  • Received: 22 March 2024 Revised: 30 April 2024 Accepted: 14 May 2024 Published: 31 July 2024
  • MSC : 53C21, 53C25, 53C50

  • Our investigation involved sequentially warped product manifolds that contained gradient-normalized Ricci-harmonic solitons. We presented the primary connections for a gradient-normalized Ricci-harmonic soliton on sequential warped product manifolds. In practical applications, our research investigated gradient-normalized Ricci-harmonic solitons for sequential generalized Robertson-Walker spacetimes and sequential standard static space-times. Our finding generalized all results proven in [26].

    Citation: Noura Alhouiti, Fatemah Mofarreh, Akram Ali, Fatemah Abdullah Alghamdi. On gradient normalized Ricci-harmonic solitons in sequential warped products[J]. AIMS Mathematics, 2024, 9(9): 23221-23233. doi: 10.3934/math.20241129

    Related Papers:

  • Our investigation involved sequentially warped product manifolds that contained gradient-normalized Ricci-harmonic solitons. We presented the primary connections for a gradient-normalized Ricci-harmonic soliton on sequential warped product manifolds. In practical applications, our research investigated gradient-normalized Ricci-harmonic solitons for sequential generalized Robertson-Walker spacetimes and sequential standard static space-times. Our finding generalized all results proven in [26].



    加载中


    [1] A. Abolarinwa, Evolution and monotonicity of the first eigenvalue of $p$-Laplacian under the Ricci-harmonic flow, J. Appl. Anal., 21 (2015), 147–160. https://doi.org/10.1515/jaa-2015-0013 doi: 10.1515/jaa-2015-0013
    [2] A. Abolarinwa, Gap theorems for compact almost Ricci-harmonic solitons, Int. J. Math., 30 (2019), 1950040. https://doi.org/10.1142/S0129167X1950040X doi: 10.1142/S0129167X1950040X
    [3] A. Abolarinwa, N. K. Oladejo, S. O. Salawu, On the entropy formulas and solitons for the Ricci-harmonic flow, Bull. Iran. Math. Soc., 45 (2019), 1177–1192. https://doi.org/10.1007/s41980-018-00192-1 doi: 10.1007/s41980-018-00192-1
    [4] A. Abolarinwa, Y. Chong, D. Zhang, On the spectrum of the $p$-biharmonic operator under the Ricci flow, Results Math., 75 (2020), 54. https://doi.org/10.1007/s00025-020-1182-9 doi: 10.1007/s00025-020-1182-9
    [5] A. Anselli, On the rigidity of harmonic-Ricci solitons, Adv. Geom., 22 (2022), 171–198. https://doi.org/10.1515/advgeom-2022-0003 doi: 10.1515/advgeom-2022-0003
    [6] S. Azami, Ricci-Bourguignon flow coupled with harmonic map flow, Int. J. Math., 30 (2019), 1950049. https://doi.org/10.1142/S0129167X19500496 doi: 10.1142/S0129167X19500496
    [7] S. Azami, V. Pirhadi, G. Fasihi-Ramandi, Complete shrinking Ricci-Bourguignon harmonic solitons, Int. J. Math., 33 (2022), 2250046. https://doi.org/10.1142/S0129167X2250046X doi: 10.1142/S0129167X2250046X
    [8] H. Al-Sodais, H. Alodan, S. Deshmukh, Hypersurfaces of Euclidean space as gradient Ricci solitons, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (NS), 61 (2015), 437–444.
    [9] A. Ali, F. Mofarreh, D. S. Patra, Geometry of almost Ricci solitons on paracontact metric manifolds, Quaest. Math., 45 (2022), 1167–1180. https://doi.org/10.2989/16073606.2021.1929539 doi: 10.2989/16073606.2021.1929539
    [10] A. Ali, N. Alshehri, F. Mofarreh, Y. Li, Geometry of gradient Einstein harmonic solitons in sequential warped products manifolds, Eur. Phys. J. Plus, 139 (2024), 339. https://doi.org/10.1140/epjp/s13360-024-05120-3 doi: 10.1140/epjp/s13360-024-05120-3
    [11] R. L. Bishop, B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1–49.
    [12] A. M. Blaga, H. M. Tastan, Gradient solitons on doubly warped product manifolds, Rep. Math. Phys., 89 (2022), 319–333. https://doi.org/10.1016/S0034-4877(22)00036-2 doi: 10.1016/S0034-4877(22)00036-2
    [13] U. C. De, M. Turan, A. Yildiz, A. De, Ricci solitons and gradient Ricci solitons on $3$-dimensional normal almost contact metric manifolds, Publ. Math. Debrecen, 80 (2012), 127–142.
    [14] U. C. De, K. Mandal, Ricci solitons and gradient Ricci solitons on N($ k $)-paracontact manifold, Zh. Mat. Fiz. Anal. Geom., 15 (2019), 307–320. https://doi.org/10.15407/mag15.03.307 doi: 10.15407/mag15.03.307
    [15] S. Dwivedi, Some results on Ricci-Bourguignon solitons and almost solitons, Can. Math. Bull., 64 (2021), 591–604. https://doi.org/10.4153/S0008439520000673 doi: 10.4153/S0008439520000673
    [16] S. Dwivedi, D. S. Patra, Some results on almost $*$-Ricci-Bourguignon solitons, J. Geom. Phys., 178 (2022), 104519. https://doi.org/10.1016/j.geomphys.2022.104519 doi: 10.1016/j.geomphys.2022.104519
    [17] U. C. De, S. Shenawy, Generalized quasi-Einstein GRW space-times, Int. J. Geom. Methods M., 16 (2019), 1950124. https://doi.org/10.1142/S021988781950124X doi: 10.1142/S021988781950124X
    [18] U. C. De, S. Shenawy, B. Unal, Sequential warped products: Curvature and conformal vector fields, Filomat, 33 (2019), 4071–4083. https://doi.org/10.2298/FIL1913071D doi: 10.2298/FIL1913071D
    [19] F. Dobarro, B. Unal, Special standard static space–times, Nonlinear Anal.-Theor., 59 (2004), 759–770. https://doi.org/10.1016/j.na.2004.07.035 doi: 10.1016/j.na.2004.07.035
    [20] H. X. Guo, R. Philipowski, A. Thalmaier, On gradient solitons of the Ricci-harmonic flow, Acta Math. Sin. (Engl. Ser.), 31 (2015), 1798–1804. https://doi.org/10.1007/s10114-015-4446-7 doi: 10.1007/s10114-015-4446-7
    [21] S. Guler, Sequential warped products and their applications, Int. Electron. J. Geom., 14 (2021), 277–291. https://doi.org/10.36890/iejg.937419 doi: 10.36890/iejg.937419
    [22] D. Ganguly, S. Dey, A. Ali, A. Bhattacharyya, Conformal Ricci soliton and quasi-Yamabe soliton on generalized Sasakian space form, J. Geom. Phys., 169 (2021), 104339. https://doi.org/10.1016/j.geomphys.2021.104339 doi: 10.1016/j.geomphys.2021.104339
    [23] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry, 17 (1982), 255–306. https://doi.org/10.4310/jdg/1214436922 doi: 10.4310/jdg/1214436922
    [24] R. S. Hamilton, The Ricci flow on surfaces, In: Mathematics and general relativity, Contemporary Mathematics, 1988,237–262. https://doi.org/10.1090/conm/071
    [25] F. Karaca, C. Ozgur, Gradient Ricci-harmonic solitons on doubly warped product manifolds, Filomat, 37 (2023), 5969–5977. https://doi.org/10.2298/FIL2318969K doi: 10.2298/FIL2318969K
    [26] F. Karaca, C. Ozgur, On sequential warped product manifolds admitting gradient Ricci-harmonic solitons, Phys. Scr., 98 (2023), 085213. https://doi.org/10.1088/1402-4896/ace1b4 doi: 10.1088/1402-4896/ace1b4
    [27] M. L. de Sousa, R. Pina, Gradient Ricci solitons with the structure of warped products, Results Math., 71 (2017), 825–840. https://doi.org/10.1007/s00025-016-0583-2 doi: 10.1007/s00025-016-0583-2
    [28] Y. Li, D. S. Patra, N. Alluhaibi, F. Mofarreh, A. Ali, Geometric classifications of $k$-almost Ricci solitons admitting paracontact metrices, Open Math., 21 (2023), 20220610. https://doi.org/10.1515/math-2022-0610 doi: 10.1515/math-2022-0610
    [29] R. Muller, Ricci flow coupled with harmonic map flow, 2012, arXiv: 0912.2907. https://doi.org/10.48550/arXiv.0912.2907
    [30] D. S. Patra, A. Ali, F. Mofarreh, Characterizations of Ricci-Bourguignon almost solitons on pseudo-Riemannian manifolds, Mediterr. J. Math., 19 (2022), 176. https://doi.org/10.1007/s00009-022-02085-4 doi: 10.1007/s00009-022-02085-4
    [31] X. Cao, A remark of Ricci-Bourguignon harmonic soliton, 2023, arXiv: 2309.16485. https://doi.org/10.48550/arXiv.2309.16485
  • Reader Comments
  • © 2024 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(562) PDF downloads(60) Cited by(0)

Article outline

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog