On Einstein-type almost Kenmotsu manifolds

References

[1] L. Ambrozio, On static three-manifolds with positive scalar curvature, J. Differential Geom. 107 (2017), no. 1, 1–45. 10.4310/jdg/1505268028Suche in Google Scholar

[2] H. Baltazar, On critical point equation of compact manifolds with zero radial Weyl curvature, Geom. Dedicata 202 (2019), 337–355. 10.1007/s10711-018-0417-3Suche in Google Scholar

[3] A. Barros and E. Ribeiro, Jr., Critical point equation on four-dimensional compact manifolds, Math. Nachr. 287 (2014), no. 14–15, 1618–1623. 10.1002/mana.201300149Suche in Google Scholar

[4] A. L. Besse, Einstein Manifolds, Class. Math., Springer, Berlin, 2008. Suche in Google Scholar

[5] P. Cernea and D. Guan, Killing fields generated by multiple solutions to the Fischer–Marsden equation, Internat. J. Math. 26 (2015), no. 4, 93–111. 10.1142/S0129167X15400066Suche in Google Scholar

[6] S. K. Chaubey, U. C. De and Y. J. Suh, Kenmotsu manifolds satisfying the Fischer–Marsden equation, J. Korean Math. Soc. 58 (2021), no. 3, 597–607. Suche in Google Scholar

[7] U. C. De and K. Mandal, The Fischer–Marsden conjecture on almost Kenmotsu manifolds, Quaest. Math. 43 (2020), no. 1, 25–33. 10.2989/16073606.2018.1533499Suche in Google Scholar

[8] G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 2, 343–354. 10.36045/bbms/1179839227Suche in Google Scholar

[9] G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93 (2009), no. 1–2, 46–61. 10.1007/s00022-009-1974-2Suche in Google Scholar

[10] A. E. Fischer and J. E. Marsden, Manifolds of Riemannian metrics with prescribed scalar curvature, Bull. Amer. Math. Soc. 80 (1974), 479–484. 10.1090/S0002-9904-1974-13457-9Suche in Google Scholar

[11] A. Ghosh and D. S. Patra, The critical point equation and contact geometry, J. Geom. 108 (2017), no. 1, 185–194. 10.1007/s00022-016-0333-3Suche in Google Scholar

[12] A. Ghosh and D. S. Patra, Certain almost Kenmotsu metrics satisfying the Miao-Tam equation, Publ. Math. Debrecen 93 (2018), no. 1–2, 107–123. 10.5486/PMD.2018.8075Suche in Google Scholar

[13] S. Hwang, Critical points of the total scalar curvature functional on the space of metrics of constant scalar curvature, Manuscripta Math. 103 (2000), no. 2, 135–142. 10.1007/PL00005857Suche in Google Scholar

[14] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. (2) 24 (1972), 93–103. 10.2748/tmj/1178241594Suche in Google Scholar

[15] O. Kobayashi and M. Obata, Conformally-flatness and static space-time, Manifolds and Lie Groups, Progr. Math. 14, Birkhäuser, Boston (1981), 197–206. 10.1007/978-1-4612-5987-9_10Suche in Google Scholar

[16] H. A. Kumara and V. Venkatesha, Gradient Einstein-type contact metric manifolds, Commun. Korean Math. Soc. 35 (2020), no. 2, 639–651. Suche in Google Scholar

[17] H. A. Kumara, V. Venkatesha and D. M. Naik, Static perfect fluid space-time on almost Kenmotsu manifolds, J. Geom. Symmetry Phys. 61 (2021), 41–51. 10.7546/jgsp-61-2021-41-51Suche in Google Scholar

[18] B. Leandro, Vanishing conditions on Weyl tensor for Einstein-type manifolds, Pacific J. Math. 314 (2021), no. 1, 99–113. 10.2140/pjm.2021.314.99Suche in Google Scholar

[19] P. Miao and L.-F. Tam, On the volume functional of compact manifolds with boundary with constant scalar curvature, Calc. Var. Partial Differential Equations 36 (2009), no. 2, 141–171. 10.1007/s00526-008-0221-2Suche in Google Scholar

[20] D. M. Naik, V. Venkatesha and H. A. Kumara, Some results on almost Kenmotsu manifolds, Note Mat. 40 (2020), no. 1, 87–100. Suche in Google Scholar

[21] D. S. Patra and A. Ghosh, On Einstein-type contact metric manifolds, J. Geom. Phys. 169 (2021), Paper No. 104342. 10.1016/j.geomphys.2021.104342Suche in Google Scholar

[22] D. S. Patra, A. Ghosh and A. Bhattacharyya, The critical point equation on Kenmotsu and almost Kenmotsu manifolds, Publ. Math. Debrecen 97 (2020), no. 1–2, 85–99. 10.5486/PMD.2020.8702Suche in Google Scholar

[23] D. G. Prakasha, P. Veeresha and Venkatesha, The Fischer–Marsden conjecture on non-Kenmotsu ( κ , μ ) ′ -almost Kenmotsu manifolds, J. Geom. 110 (2019), no. 1, Paper No. 1. 10.1007/s00022-018-0457-8Suche in Google Scholar

[24] J. Qing and W. Yuan, A note on static spaces and related problems, J. Geom. Phys. 74 (2013), 18–27. 10.1016/j.geomphys.2013.07.003Suche in Google Scholar

[25] Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc. 117 (1965), 251–275. 10.1090/S0002-9947-1965-0174022-6Suche in Google Scholar

[26] L. Vanhecke and D. Janssens, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), no. 1, 1–27. 10.2996/kmj/1138036310Suche in Google Scholar

[27] V. Venkatesha and H. A. Kumara, Gradient ρ-Einstein soliton on almost Kenmotsu manifolds, Ann. Univ. Ferrara Sez. VII Sci. Mat. 65 (2019), no. 2, 375–388. 10.1007/s11565-019-00323-4Suche in Google Scholar

[28] V. Venkatesha, H. A. Kumara and D. M. Naik, Riemann solitons and almost Riemann solitons on almost Kenmotsu manifolds, Int. J. Geom. Methods Mod. Phys. 17 (2020), no. 7, Article ID 2050105. 10.1142/S0219887820501054Suche in Google Scholar

[29] V. Venkatesha, H. A. Kumara and D. M. Naik, Ricci recurrent almost Kenmotsu 3-manifolds, Filomat 35 (2021), no. 7, 2293–2301. 10.2298/FIL2107293VSuche in Google Scholar

[30] V. Venkatesha, D. M. Naik and H. A. Kumara, * -Ricci solitons and gradient almost * -Ricci solitons on Kenmotsu manifolds, Math. Slovaca 69 (2019), no. 6, 1447–1458. 10.1515/ms-2017-0321Suche in Google Scholar

[31] Y. Wang and X. Liu, On almost Kenmotsu manifolds satisfying some nullity distributions, Proc. Nat. Acad. Sci. India Sect. A 86 (2016), no. 3, 347–353. 10.1007/s40010-016-0274-0Suche in Google Scholar

[32] Y. Wang and W. Wang, An Einstein-like metric on almost Kenmotsu manifolds, Filomat 31 (2017), no. 15, 4695–4702. 10.2298/FIL1715695WSuche in Google Scholar