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Year 2020, Volume: 8 Issue: 1, 70 - 78, 15.04.2020

M.d. Siddiqi S. K. Chaubey

Abstract

References

  • [1] S. R. Ashoka, C. S. Bagewadi and G. Ingalahlli, A geometry on Ricci soliton in (LCS)n-manifolds, Differential Geometry-Dynamical System, 16, (2014), 50-62.
  • [2] N. Basu and A. Bhattacharyya, Conformal Ricci soliton in Kenmotsu manifold, Global Journal of Advanced Research on Classical and Modern Geometries, 4, (2015), 159-621.
  • [3] A. M. Blaga, h-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30 (2), (2016), 489-496.
  • [4] A. M. Blaga, h-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20, (2015), 1-13.
  • [5] C. S. Bagewadi and G. Ingalahalli, Ricci Solitons in Lorentzian a-Sasakian Manifolds, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 28 (1), (2012), 59-68.
  • [6] A. Bhattacharyya and N. Basu, Some curvature identities on Gradient Shrinking Conformal Ricci Soliton, Analele Stiintice Ale Universitatii Al.I.Cuza Din Iasi (S.N) Mathematica, 61 (1), (2015), 245-252.
  • [7] X. Cao, Compact Gradient Shrinking Ricci Solitons with positive curvature operator, J. Geom. Anal., 17 (3), (2007), 425-433.
  • [8] C. Calin and M. Crasmareanu, h-Ricci solitons on Hopf Hypersurfaces in complex space forms, Rev. Roumaine Math. Pures Appl., 57 (1), (2012), 55-63.
  • [9] S. K. Chaubey, On special weakly Ricci-symmetric and generalized Ricci-recurrent trans-Sasakian manifolds, Thai Journal of Mathematics, 18 (3), (2018), 693-707.
  • [10] S. K. Chaubey, K. K. Baishya and M. Danish Siddiqi, Existence of some classes of N(k)-quasi Einstein manifolds, Bol. Soc. Paran. Mat., doi:10.5269/bspm.41450.
  • [11] S. K. Chaubey, Certain results on N(k)-quasi Einstein manifolds, Afrika Matematika, 30 (1-2), (2019), 113-127.
  • [12] S. K. Chaubey, Existence of N(k)-quasi Einstein manifolds, Facta Universitatis (NIS) Ser. Math. Inform., 32 (3), (2017), 369-385.
  • [13] S. K. Chaubey, Trans-Sasakian manifolds satisfying certain conditions, TWMS J. App. Eng. Math. 9 (2) (2019), 305-314.
  • [14] S. K. Chaubey and A. Yildiz, On Ricci tensor in the generalized Sasakian-space-forms, International Journal of Maps in Mathematics, 2 (1), (2019), 131-147.
  • [15] S. K. Chaubey and S. K. Yadav, W-semisymmetric generalized Sasakian-space-forms, Adv. Pure Appl. Math., 10 (4), (2019), 427-436.
  • [16] S. K. Chaubey and A. A. Shaikh, On 3-dimensional Lorentzian concircular structure manifolds, Commun. Korean Math. Soc., 34 (1), (2019), 303–319.
  • [17] S. K. Chaubey, Generalized Robertson-Walker space-times withW1-curvature tensor, J. Phys. Math., 10 (2), (2019), 1000303.
  • [18] J. T. Cho and M. Kimura, Ricci solitons and Real hypersurfaces in a complex space form, Tohoku Math. J., 61, (2009), 205-212.
  • [19] U. C. De, Y. J. Suh, S. K. Chaubey and S. Shenawy, On pseudo H -symmetric Lorentzian manifolds with applications to relativity, Filomat, (2020) (Accepted).
  • [20] T. Dutta, N. Basu and A. Bhattacharyya, Conformal Ricci soliton in Lorentzian a-Sasakian manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math., 55 (2), (2016), 57-70.
  • [21] A. E. Fischer, An introduction to conformal Ricci flow, class. Quantum Grav., 21, (2004), S171-S218.
  • [22] R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, (Santa Cruz. CA, 1986), Contemp. Math. 71, Amer. Math. Soc., (1988), 237-262.
  • [23] S. K. Hui and D. Chakraborty, Some types of Ricci solitons on (LCS)n-manifolds, J. Math. Sciences: Advances and Applications, 37, (2016), 1-17.
  • [24] S. K. Hui, S. K. Yadav and S. K. Chaubey, h-Ricci soliton on 3-dimensional f-Kenmotsu manifolds, Appl. Appl. Math., 13 (2), (2018), 933-951.
  • [25] S. K. Hui and D. Chakrobarty, h-Ricci solitons on h-Einstein (LCS)n-manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 55 (2), (2016), 101-109.
  • [26] H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. Math., 27 (2), (1925), 91-98.
  • [27] K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci., 12 (2), (1989), 151–156.
  • [28] B. O’. Neill, Semi-Riemannian Geometry, Academic Press, New York, 1983.
  • [29] S. Pigola, M. Rigoli, M. Rimoldi and A. G. Setti, Ricci almost solitons, arXiv:1003.2945v1, (2010).
  • [30] G. P. Pokhariyal, S. Yadav and S. K. Chaubey, Ricci solitons on trans-Sasakian manifolds, Differential Geometry-Dynamical Systems, 20, (2018), 138-158.
  • [31] A. A. Shaikh, On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J., 43 (2), (2003), 305-314.
  • [32] A. A. Shaikh and T. Q. Binh, On weakly symmetric (LCS)n-manifolds, J. Adv. Math. Studies, 2, (2009), 75-90.
  • [33] A. A. Shaikh, Some results on (LCS)n-manifolds, J. Korean Math. Soc., 46 (3), (2009), 449-461.
  • [34] R. Sharma, Almost Ricci solitons and K-contact geometry, Monatshefte f ¨ ur MathematikMonatsh Math., 175 (4), (2014), 621-628.
  • [35] R. Sharma, Certain results on K-contact and (k;m)-contact manifolds, J. Geom., 89 (1-2), (2008), 138-147.
  • [36] M. D. Siddiqi, Ricci r-soliton and geometrical structure in a dust fluid and viscous fluid spacetime, Bulg. J. Phys., 46, (2019), 163-173.
  • [37] M. D. Siddiqi, Conformal h-Ricci solitons in d-Lorentzian trans-Sasakian manifolds, Int. J. Maps Math., 1, (2018), 15-34.
  • [38] M. Turan, C. Yetim and S. K. Chaubey, On quasi-Sasakian 3-manifolds admitting h-Ricci solitons, Filomat, 33 (15), (2019), 4923-4930.
  • [39] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Some geometric properties of h-Ricci solitons and gradient Ricci solitons on (LCS)n-manifolds, Cubo a Mathematical Journal, 2 (19), (2017), 33-48.
  • [40] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Some results of h-Ricci soliton on (LCS)n- manifolds, Surveys in Mathematics and its Applications 13 (2018), 237-250.
  • [41] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain results on almost Kenmotsu (k;m;n)-spaces, Konuralp Journal of Mathematics, 6 (1), (2018), 128-133.
  • [42] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain geometric properties of h-Ricci solitons on h-Einstein para-Kenmotsu manifolds, Palestine Journal of Mathematics, 9 (1), (2020), 237-244.
  • [43] S. K. Yadav, S. K. Chaubey and S. K. Hui, On the Perfect Fluid Lorentzian Para-Sasakian Spacetimes, Bulg. J. Phys., 46, (2019), 1-15.

Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures

Year 2020, Volume: 8 Issue: 1, 70 - 78, 15.04.2020

M.d. Siddiqi S. K. Chaubey

Abstract

The object of the present paper is to study the properties of three-dimensional Lorentzian concircular structure ($(LCS)_{3}$-)manifolds admitting the almost conformal $\eta$-Ricci solitons and gradient shrinking $\eta$-Ricci solitons. It is proved that an $(LCS)_3$-manifold with either an almost conformal $\eta$-Ricci soliton or a gradient shrinking $\eta$-Ricci soliton is a quasi-Einstein manifold. Also, the example of an almost conformal $\eta$-Ricci soliton in an $(LCS)_{3}$-manifold is provided in the region where $(LCS)_{3}$-manifold is expanding.


Keywords

$\eta$-Ricci solitons $(LCS)_{n}$-manifold Quasi Einstein manifold Einstein manifolds

References

  • [1] S. R. Ashoka, C. S. Bagewadi and G. Ingalahlli, A geometry on Ricci soliton in (LCS)n-manifolds, Differential Geometry-Dynamical System, 16, (2014), 50-62.
  • [2] N. Basu and A. Bhattacharyya, Conformal Ricci soliton in Kenmotsu manifold, Global Journal of Advanced Research on Classical and Modern Geometries, 4, (2015), 159-621.
  • [3] A. M. Blaga, h-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30 (2), (2016), 489-496.
  • [4] A. M. Blaga, h-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20, (2015), 1-13.
  • [5] C. S. Bagewadi and G. Ingalahalli, Ricci Solitons in Lorentzian a-Sasakian Manifolds, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 28 (1), (2012), 59-68.
  • [6] A. Bhattacharyya and N. Basu, Some curvature identities on Gradient Shrinking Conformal Ricci Soliton, Analele Stiintice Ale Universitatii Al.I.Cuza Din Iasi (S.N) Mathematica, 61 (1), (2015), 245-252.
  • [7] X. Cao, Compact Gradient Shrinking Ricci Solitons with positive curvature operator, J. Geom. Anal., 17 (3), (2007), 425-433.
  • [8] C. Calin and M. Crasmareanu, h-Ricci solitons on Hopf Hypersurfaces in complex space forms, Rev. Roumaine Math. Pures Appl., 57 (1), (2012), 55-63.
  • [9] S. K. Chaubey, On special weakly Ricci-symmetric and generalized Ricci-recurrent trans-Sasakian manifolds, Thai Journal of Mathematics, 18 (3), (2018), 693-707.
  • [10] S. K. Chaubey, K. K. Baishya and M. Danish Siddiqi, Existence of some classes of N(k)-quasi Einstein manifolds, Bol. Soc. Paran. Mat., doi:10.5269/bspm.41450.
  • [11] S. K. Chaubey, Certain results on N(k)-quasi Einstein manifolds, Afrika Matematika, 30 (1-2), (2019), 113-127.
  • [12] S. K. Chaubey, Existence of N(k)-quasi Einstein manifolds, Facta Universitatis (NIS) Ser. Math. Inform., 32 (3), (2017), 369-385.
  • [13] S. K. Chaubey, Trans-Sasakian manifolds satisfying certain conditions, TWMS J. App. Eng. Math. 9 (2) (2019), 305-314.
  • [14] S. K. Chaubey and A. Yildiz, On Ricci tensor in the generalized Sasakian-space-forms, International Journal of Maps in Mathematics, 2 (1), (2019), 131-147.
  • [15] S. K. Chaubey and S. K. Yadav, W-semisymmetric generalized Sasakian-space-forms, Adv. Pure Appl. Math., 10 (4), (2019), 427-436.
  • [16] S. K. Chaubey and A. A. Shaikh, On 3-dimensional Lorentzian concircular structure manifolds, Commun. Korean Math. Soc., 34 (1), (2019), 303–319.
  • [17] S. K. Chaubey, Generalized Robertson-Walker space-times withW1-curvature tensor, J. Phys. Math., 10 (2), (2019), 1000303.
  • [18] J. T. Cho and M. Kimura, Ricci solitons and Real hypersurfaces in a complex space form, Tohoku Math. J., 61, (2009), 205-212.
  • [19] U. C. De, Y. J. Suh, S. K. Chaubey and S. Shenawy, On pseudo H -symmetric Lorentzian manifolds with applications to relativity, Filomat, (2020) (Accepted).
  • [20] T. Dutta, N. Basu and A. Bhattacharyya, Conformal Ricci soliton in Lorentzian a-Sasakian manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math., 55 (2), (2016), 57-70.
  • [21] A. E. Fischer, An introduction to conformal Ricci flow, class. Quantum Grav., 21, (2004), S171-S218.
  • [22] R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, (Santa Cruz. CA, 1986), Contemp. Math. 71, Amer. Math. Soc., (1988), 237-262.
  • [23] S. K. Hui and D. Chakraborty, Some types of Ricci solitons on (LCS)n-manifolds, J. Math. Sciences: Advances and Applications, 37, (2016), 1-17.
  • [24] S. K. Hui, S. K. Yadav and S. K. Chaubey, h-Ricci soliton on 3-dimensional f-Kenmotsu manifolds, Appl. Appl. Math., 13 (2), (2018), 933-951.
  • [25] S. K. Hui and D. Chakrobarty, h-Ricci solitons on h-Einstein (LCS)n-manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 55 (2), (2016), 101-109.
  • [26] H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. Math., 27 (2), (1925), 91-98.
  • [27] K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci., 12 (2), (1989), 151–156.
  • [28] B. O’. Neill, Semi-Riemannian Geometry, Academic Press, New York, 1983.
  • [29] S. Pigola, M. Rigoli, M. Rimoldi and A. G. Setti, Ricci almost solitons, arXiv:1003.2945v1, (2010).
  • [30] G. P. Pokhariyal, S. Yadav and S. K. Chaubey, Ricci solitons on trans-Sasakian manifolds, Differential Geometry-Dynamical Systems, 20, (2018), 138-158.
  • [31] A. A. Shaikh, On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J., 43 (2), (2003), 305-314.
  • [32] A. A. Shaikh and T. Q. Binh, On weakly symmetric (LCS)n-manifolds, J. Adv. Math. Studies, 2, (2009), 75-90.
  • [33] A. A. Shaikh, Some results on (LCS)n-manifolds, J. Korean Math. Soc., 46 (3), (2009), 449-461.
  • [34] R. Sharma, Almost Ricci solitons and K-contact geometry, Monatshefte f ¨ ur MathematikMonatsh Math., 175 (4), (2014), 621-628.
  • [35] R. Sharma, Certain results on K-contact and (k;m)-contact manifolds, J. Geom., 89 (1-2), (2008), 138-147.
  • [36] M. D. Siddiqi, Ricci r-soliton and geometrical structure in a dust fluid and viscous fluid spacetime, Bulg. J. Phys., 46, (2019), 163-173.
  • [37] M. D. Siddiqi, Conformal h-Ricci solitons in d-Lorentzian trans-Sasakian manifolds, Int. J. Maps Math., 1, (2018), 15-34.
  • [38] M. Turan, C. Yetim and S. K. Chaubey, On quasi-Sasakian 3-manifolds admitting h-Ricci solitons, Filomat, 33 (15), (2019), 4923-4930.
  • [39] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Some geometric properties of h-Ricci solitons and gradient Ricci solitons on (LCS)n-manifolds, Cubo a Mathematical Journal, 2 (19), (2017), 33-48.
  • [40] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Some results of h-Ricci soliton on (LCS)n- manifolds, Surveys in Mathematics and its Applications 13 (2018), 237-250.
  • [41] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain results on almost Kenmotsu (k;m;n)-spaces, Konuralp Journal of Mathematics, 6 (1), (2018), 128-133.
  • [42] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain geometric properties of h-Ricci solitons on h-Einstein para-Kenmotsu manifolds, Palestine Journal of Mathematics, 9 (1), (2020), 237-244.
  • [43] S. K. Yadav, S. K. Chaubey and S. K. Hui, On the Perfect Fluid Lorentzian Para-Sasakian Spacetimes, Bulg. J. Phys., 46, (2019), 1-15.
There are 43 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

M.d. Siddiqi This is me

S. K. Chaubey

Publication Date April 15, 2020
Submission Date June 18, 2019
Acceptance Date April 2, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Siddiqi, M., & Chaubey, S. K. (2020). Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures. Konuralp Journal of Mathematics, 8(1), 70-78.
AMA Siddiqi M, Chaubey SK. Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures. Konuralp J. Math. April 2020;8(1):70-78.
Chicago Siddiqi, M.d., and S. K. Chaubey. “Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 70-78.
EndNote Siddiqi M, Chaubey SK (April 1, 2020) Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures. Konuralp Journal of Mathematics 8 1 70–78.
IEEE M. Siddiqi and S. K. Chaubey, “Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures”, Konuralp J. Math., vol. 8, no. 1, pp. 70–78, 2020.
ISNAD Siddiqi, M.d. - Chaubey, S. K. “Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures”. Konuralp Journal of Mathematics 8/1 (April 2020), 70-78.
JAMA Siddiqi M, Chaubey SK. Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures. Konuralp J. Math. 2020;8:70–78.
MLA Siddiqi, M.d. and S. K. Chaubey. “Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 70-78.
Vancouver Siddiqi M, Chaubey SK. Almost Conformal $\eta$-Ricci Solitons in Three-Dimensional Lorentzian Concircular Structures. Konuralp J. Math. 2020;8(1):70-8.
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