Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOLITONS OF KÄHLERIAN NORDEN SPACE-TIME MANIFOLDS

  • Received : 2020.12.18
  • Accepted : 2021.11.16
  • Published : 2022.07.31
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Abstract

We study solitons of Kählerian Norden space-time manifolds and Bochner curvature tensor in almost pseudo symmetric Kählerian space-time manifolds. It is shown that the steady, expanding or shrinking solitons depend on different relations of energy density/isotropic pressure, the cosmological constant, and gravitational constant.

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References

  1. N. Basu and A. Bhattacharyya, Conformal Ricci soliton in Kenmotsu manifold, Glob. J. Adv. Res. Class. Mod. Geom. 4 (2015), no. 1, 15-21.
  2. A. M. Blaga, On gradient η-Einstein solitons, Kragujevac J. Math. 42 (2018), no. 2, 229-237. https://doi.org/10.5937/kgjmath1802229b
  3. A. M. Blaga, Solitons and geometrical structures in a perfect fluid spacetime, Rocky Mountain J. Math. 50 (2020), no. 1, 41-53. https://doi.org/10.1216/rmj.2020.50.41
  4. A. M. Blaga, A. Ishan, and S. Deshmukh, A note on solitons with generalized geodesic vector field, Symmetry 13 (2021), no. 7, 1104. https://doi.org/10.3390/sym13071104
  5. G. Catino and L. Mazzieri, Gradient Einstein solitons, Nonlinear Anal. 132 (2016), 66-94. https://doi.org/10.1016/j.na.2015.10.021
  6. M. C. Chaki and R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen 57 (2000), no. 3-4, 297-306. https://doi.org/10.5486/PMD.2000.2169
  7. M. C. Chaki and S. Ray, Space-times with covariant-constant energy-momentum tensor, Internat. J. Theoret. Phys. 35 (1996), no. 5, 1027-1032. https://doi.org/10.1007/BF02302387
  8. J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. (2) 61 (2009), no. 2, 205-212. https://doi.org/10.2748/tmj/1245849443
  9. B. Chow, P. Lu, and L. Ni, Hamilton's Ricci Flow, Graduate Studies in Mathematics, 77, American Mathematical Society, Providence, RI, 2006. https://doi.org/10.1090/gsm/077
  10. U. C. De and A. K. Gazi, On almost pseudo symmetric manifolds, Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 51 (2008), 53-68 (2009).
  11. U. C. De and G. C. Ghosh, On weakly Ricci symmetric spacetime manifolds, Rad. Mat. 13 (2004), no. 1, 93-101.
  12. G. T. Ganchev and A. V. Borisov, Note on the almost complex manifolds with a Norden metric, C. R. Acad. Bulgare Sci. 39 (1986), no. 5, 31-34.
  13. R. S. Hamilton, The Ricci flow on surfaces, in Mathematics and general relativity (Santa Cruz, CA, 1986), 237-262, Contemp. Math., 71, Amer. Math. Soc., Providence, RI, 1988. https://doi.org/10.1090/conm/071/954419
  14. K. M. Haradhan, Minkowski geometry and space-time manifold in relativity, J. Environmental Treatment Techniques 1 (2013), no. 2, 101-110.
  15. V. R. Kaigorodov, Structure of the curvature of space-time, in Problems in geometry, Vol. 14, 177-204, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1983.
  16. D. M. Naik and V. Venkatesha, η-Ricci solitons and almost η-Ricci solitons on para-Sasakian manifolds, Int. J. Geom. Methods Mod. Phys. 16 (2019), no. 9, 1950134, 18 pp. https://doi.org/10.1142/S0219887819501342
  17. D. M. Naik, V. Venkatesha, and H. A. Kumara, Ricci solitons and certain related metrics on almost co-Kaehler manifolds, Zh. Mat. Fiz. Anal. Geom. 16 (2020), no. 4, 402-417. https://doi.org/10.15407/mag16.04.402
  18. B. O'Neill, Semi-Riemannian Geometry, Pure and Applied Mathematics, 103, Academic Press, Inc., New York, 1983.
  19. M. M. Praveena and C. S. Bagewadi, On almost pseudo Bochner symmetric generalized complex space forms, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 32 (2016), no. 1, 149-159.
  20. M. M. Praveena and C. S. Bagewadi, On almost pseudo symmetric Kahler manifolds, Palest. J. Math. 6 (2017), Special Issue II, 272-278.
  21. M. M. Praveena, C. S. Bagewadi, and M. R. Krishnamurthy, Solitons of Kahlerian space-time manifolds, Int. J. Geom. Methods Mod. Phys. 18 (2021), no. 2, Paper No. 2150021, 12 pp. https://doi.org/10.1142/S0219887821500213
  22. A. K. Raychaudhuri, S. Banerji, and A. Banerjee, General Relativity, Astrophysics, and Cosmology, Astronomy and Astrophysics Library, Springer-Verlag, New York, 1992.
  23. A. A. Shaikh, D. W. Yoon, and S. K. Hui, On quasi-Einstein spacetimes, Tsukuba J. Math. 33 (2009), no. 2, 305-326. https://doi.org/10.21099/tkbjm/1267209423
  24. Mohd. D. Siddiqi and S. A. Siddiqui, Conformal Ricci soliton and geometrical structure in a perfect fluid spacetime, Int. J. Geom. Methods Mod. Phys. 17 (2020), no. 6, 2050083, 18 pp. https://doi.org/10.1142/S0219887820500838
  25. Venkatesha and H. A. Kumara, Ricci soliton and geometrical structure in a perfect fluid spacetime with torse-forming vector field, Afr. Mat. 30 (2019), no. 5-6, 725-736. https://doi.org/10.1007/s13370-019-00679-y
  26. Venkatesha and H. A. Kumara, A study of conformally flat quasi-Einstein spacetimes with applications in general relativity, Kragujevac J. Math. 45 (2021), no. 3, 477-489. https://doi.org/10.46793/kgjmat2103.477v
  27. K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publishing Co., Singapore, 1984.