Conformal Ricci Soliton in Lorentzian α -Sasakian Manifolds

Tamalika Dutta; Nirabhra Basu; Arindam BHATTACHARYYA

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 2, page 57-70
  • ISSN: 0231-9721

Abstract

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In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian α -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian α -Sasakian manifold admitting conformal Ricci soliton is η -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian α -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian α -Sasakian manifold M with projective curvature tensor admitting conformal Ricci soliton is η -Einstein manifold. We have also established an example of 3-dimensional Lorentzian α -Sasakian manifold.

How to cite

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Dutta, Tamalika, Basu, Nirabhra, and BHATTACHARYYA, Arindam. "Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.2 (2016): 57-70. <http://eudml.org/doc/287916>.

@article{Dutta2016,
abstract = {In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian $\alpha $-Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian $\alpha $-Sasakian manifold admitting conformal Ricci soliton is $\eta $-Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian $\alpha $-Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian $\alpha $-Sasakian manifold $M$ with projective curvature tensor admitting conformal Ricci soliton is $\eta $-Einstein manifold. We have also established an example of 3-dimensional Lorentzian $\alpha $-Sasakian manifold.},
author = {Dutta, Tamalika, Basu, Nirabhra, BHATTACHARYYA, Arindam},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Conformal Ricci soliton; conformal curvature tensor; conharmonic curvature tensor; Lorentzian $\alpha $-Sasakian manifolds; projective curvature tensor},
language = {eng},
number = {2},
pages = {57-70},
publisher = {Palacký University Olomouc},
title = {Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds},
url = {http://eudml.org/doc/287916},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Dutta, Tamalika
AU - Basu, Nirabhra
AU - BHATTACHARYYA, Arindam
TI - Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 2
SP - 57
EP - 70
AB - In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian $\alpha $-Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian $\alpha $-Sasakian manifold admitting conformal Ricci soliton is $\eta $-Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian $\alpha $-Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian $\alpha $-Sasakian manifold $M$ with projective curvature tensor admitting conformal Ricci soliton is $\eta $-Einstein manifold. We have also established an example of 3-dimensional Lorentzian $\alpha $-Sasakian manifold.
LA - eng
KW - Conformal Ricci soliton; conformal curvature tensor; conharmonic curvature tensor; Lorentzian $\alpha $-Sasakian manifolds; projective curvature tensor
UR - http://eudml.org/doc/287916
ER -

References

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  1. Bagewadi, C. S., Ingalahalli, G., Ricci solitons in Lorentzian α -Sasakian manifolds, . Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 28 (2012), 59–68. (2012) Zbl1265.53036MR2942704
  2. Bagewadi, C. S., :, Venkatesha, Some curvature tensors on a trans-Sasakian manifold, . Turk. J. Math. 31 (2007), 111–121. (2007) Zbl1138.53028MR2335656
  3. Basu, N., Bhattacharyya, A., Conformal Ricci soliton in Kenmotsu manifold, . Global Journal of Advanced Research on Classical and Modern Geometries 4 (2015), 15–21. (2015) MR3343178
  4. Bejan, C. L., Crasmareanu, M., 10.5486/PMD.2011.4797, . Publ. Math. Debrecen 78, 1 (2011), 235–243. (2011) Zbl1274.53097MR2777674DOI10.5486/PMD.2011.4797
  5. Dutta, T., Basu, N., Bhattacharyya, A., 10.1080/1726037X.2015.1076221, . Journal of Dynamical Systems and Geometric Theories 13, 2 (2015), 163–178. (2015) MR3427160DOI10.1080/1726037X.2015.1076221
  6. Dutta, T., Basu, N., Bhattacharyya, A., Almost conformal Ricci solitons on 3 -dimensional trans-Sasakian manifold, . Hacettepe Journal of Mathematics and Statistics 45, 5 (2016), 1379–1392. (2016) Zbl1369.53021MR3699549
  7. Dutta, T., Bhattacharyya, A., Debnath, S., Conformal Ricci soliton in almost C( λ ) manifold, . Internat. J. Math. Combin. 3 (2016), 17–26. (2016) 
  8. Dwivedi, M. K., Kim, J.-S., On conharmonic curvature tensor in K-contact and Sasakian manifolds, . Bulletin of the Malaysian Mathematical Sciences Society 34, 1 (2011), 171–180. (2011) Zbl1207.53040MR2783789
  9. Fischer, A. E., 10.1088/0264-9381/21/3/011, . class.Quantum Grav. 21 (2004), S171–S218. (2004) Zbl1050.53029MR2053005DOI10.1088/0264-9381/21/3/011
  10. Formella, S., Mikeš, J., Geodesic mappings of Einstein spaces, . Ann. Sci. Stetinenses 9 (1994), 31–40. (1994) 
  11. Hamilton, R. S., 10.4310/jdg/1214436922, . J. Differential Geom. 17, 2 (1982), 255–306. (1982) MR0664497DOI10.4310/jdg/1214436922
  12. Hamilton, R. S., 10.1090/conm/071/954419, . Contemporary Mathematics 71 (1988), 237–261. (1988) Zbl0663.53031MR0954419DOI10.1090/conm/071/954419
  13. Hinterleitner, I., Mikeš, J., Geodesic mappings and Einstein spaces, . In: Geometric Methods in Physics, Trends in Mathematics, Birkhäuser, Basel, 2013, 331–335. (2013) Zbl1268.53049MR3364052
  14. Hinterleitner, I., Kiosak, V., ϕ ( R i c ) -vektor fields in Riemannian spaces, . Arch. Math. 5 (2008), 385–390. (2008) MR2501574
  15. Hinterleitner, I., Kiosak, V., ϕ ( R i c ) -vector fields on conformally flat spaces, . AIP Conf. Proc. 1191 (2009), 98–103. (2009) 
  16. Hinterleitner, I., Mikeš, J., Geodesic mappings onto Weyl manifolds, . J. Appl. Math. 2, 1 (2009), 125–133; In: Proc. 8th Int. Conf. on Appl. Math. (APLIMAT 2009), Slovak University of Technology, Bratislava, 2009, 423–430. (2009) 
  17. Mikeš, J., Geodesic mappings of semisymmetric Riemannian spaces, . Archives at VINITI, Odessk. Univ., Moscow, 1976. (1976) 
  18. Mikeš, J., Vanžurová, A., Hinterleitner, I., Geodesic Mappings and Some Generalizations, . Palacky Univ. Press, Olomouc, 2009. (2009) Zbl1222.53002MR2682926
  19. Mikeš, J., Differential Geometry of Special Mappings, . Palacky Univ. Press, Olomouc, 2015. (2015) Zbl1337.53001MR3442960
  20. Mikeš, J., Starko, G. A., On hyperbolically Sasakian and equidistant hyperbolically Kählerian spaces, . Ukr. Geom. Sb. 32 (1989), 92–98. (1989) Zbl0711.53042MR1049372
  21. Mikeš, J., On Sasaki spaces and equidistant Kähler spaces, . Sov. Math., Dokl. 34 (1987), 428–431. (1987) Zbl0631.53018MR0819428
  22. Mikeš, J., 10.1007/BF02365193, . J. Math. Sci. 78, 3 (1996), 311–333. (1996) MR1384327DOI10.1007/BF02365193
  23. Mikeš, J., 10.1007/BF01157926, . Math. Notes 28 (1981), 622–624; Transl. from: Mat. Zametki 28 (1980), 313–317. (1981) MR0587405DOI10.1007/BF01157926
  24. Mikeš, J., Geodesic mappings of m -symmetric and generalized semisymmetric spaces, . Russian Math. (Iz. VUZ) 36, 8 (1992), 38–42. (1992) MR1233688
  25. Mikeš, J., Geodesic mappings on semisymmetric spaces, . Russian Math. (Iz. VUZ) 38, 2 (1994), 35–41. (1994) MR1302090
  26. Mikeš, J., 10.1007/BF01158415, . Math. Notes 38 (1985), 855–858. (1985) Zbl0594.53024MR0819428DOI10.1007/BF01158415
  27. Sekigawa, K., 10.2996/kmj/1138036068, . Kodai Math. J. 2 (1979), 384–405. (1979) Zbl0423.53030MR0553243DOI10.2996/kmj/1138036068
  28. Sharma, R., 10.1007/s00605-014-0657-8, . Monatsh. Math. 175 (2014), 621–628. (2014) Zbl1307.53038MR3273671DOI10.1007/s00605-014-0657-8
  29. Sinyukov, N. S., Geodesic Mappings of Riemannian Spaces, . Nauka, Moscow, 1979. (1979) Zbl0637.53020
  30. Szabo, Z. I., 10.4310/jdg/1214437486, . J. Diff. Geom. 17 (1982), 531–582. (1982) MR0683165DOI10.4310/jdg/1214437486
  31. Tripathi, M. M., Ricci solitons in contact metric manifolds, . arXiv:0801,4222v1 [mathDG] 2008 (2008), 1–6. (2008) 
  32. Yadav, S., Suthar, D. L., Certain derivation on Lorentzian α -Sasakian manifold, . Global Journal of Science Frontier Research Mathematics and Decision Sciences 12, 2 (2012), 1–6. (2012) MR2814463

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