| Title:
|
Conformal Ricci Soliton in Lorentzian $\alpha $-Sasakian Manifolds (English) |
| Author:
|
Dutta, Tamalika |
| Author:
|
Basu, Nirabhra |
| Author:
|
BHATTACHARYYA, Arindam |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
57-70 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Conformal Ricci soliton |
| Keyword:
|
conformal curvature tensor |
| Keyword:
|
conharmonic curvature tensor |
| Keyword:
|
Lorentzian $\alpha $-Sasakian manifolds |
| Keyword:
|
projective curvature tensor |
| MSC:
|
53C25 |
| MSC:
|
53C44 |
| MSC:
|
53D10 |
| idZBL:
|
Zbl 1365.53046 |
| . |
| Date available:
|
2017-03-16T12:41:39Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146061 |
| . |
| Reference:
|
[1] Bagewadi, C. S., Ingalahalli, G.: Ricci solitons in Lorentzian $\alpha $-Sasakian manifolds.. Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 28 (2012), 59–68. Zbl 1265.53036, MR 2942704 |
| Reference:
|
[2] Bagewadi, C. S., :, Venkatesha: Some curvature tensors on a trans-Sasakian manifold.. Turk. J. Math. 31 (2007), 111–121. Zbl 1138.53028, MR 2335656 |
| Reference:
|
[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. MR 3343178 |
| Reference:
|
[4] Bejan, C. L., Crasmareanu, M.: Ricci solitons in manifolds with quasi-constant curvature.. Publ. Math. Debrecen 78, 1 (2011), 235–243. Zbl 1274.53097, MR 2777674, 10.5486/PMD.2011.4797 |
| Reference:
|
[5] Dutta, T., Basu, N., Bhattacharyya, A.: Some curvature identities on an almost conformal gradient shrinking Ricci soliton.. Journal of Dynamical Systems and Geometric Theories 13, 2 (2015), 163–178. MR 3427160, 10.1080/1726037X.2015.1076221 |
| Reference:
|
[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. Zbl 1369.53021, MR 3699549 |
| Reference:
|
[7] Dutta, T., Bhattacharyya, A., Debnath, S.: Conformal Ricci soliton in almost C($\lambda $) manifold.. Internat. J. Math. Combin. 3 (2016), 17–26. |
| Reference:
|
[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. Zbl 1207.53040, MR 2783789 |
| Reference:
|
[9] Fischer, A. E.: An introduction to conformal Ricci flow.. class.Quantum Grav. 21 (2004), S171–S218. Zbl 1050.53029, MR 2053005, 10.1088/0264-9381/21/3/011 |
| Reference:
|
[10] Formella, S., Mikeš, J.: Geodesic mappings of Einstein spaces.. Ann. Sci. Stetinenses 9 (1994), 31–40. |
| Reference:
|
[11] Hamilton, R. S.: Three Manifold with positive Ricci curvature.. J. Differential Geom. 17, 2 (1982), 255–306. MR 0664497, 10.4310/jdg/1214436922 |
| Reference:
|
[12] Hamilton, R. S.: The Ricci flow on surfaces.. Contemporary Mathematics 71 (1988), 237–261. Zbl 0663.53031, MR 0954419, 10.1090/conm/071/954419 |
| Reference:
|
[13] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces.. In: Geometric Methods in Physics, Trends in Mathematics, Birkhäuser, Basel, 2013, 331–335. Zbl 1268.53049, MR 3364052 |
| Reference:
|
[14] Hinterleitner, I., Kiosak, V.: $\varphi (Ric)$-vektor fields in Riemannian spaces.. Arch. Math. 5 (2008), 385–390. MR 2501574 |
| Reference:
|
[15] Hinterleitner, I., Kiosak, V.: $\varphi (Ric)$-vector fields on conformally flat spaces.. AIP Conf. Proc. 1191 (2009), 98–103. |
| Reference:
|
[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. |
| Reference:
|
[17] Mikeš, J.: Geodesic mappings of semisymmetric Riemannian spaces.. Archives at VINITI, Odessk. Univ., Moscow, 1976. |
| Reference:
|
[18] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations.. Palacky Univ. Press, Olomouc, 2009. Zbl 1222.53002, MR 2682926 |
| Reference:
|
[19] Mikeš, J.: Differential Geometry of Special Mappings.. Palacky Univ. Press, Olomouc, 2015. Zbl 1337.53001, MR 3442960 |
| Reference:
|
[20] Mikeš, J., Starko, G. A.: On hyperbolically Sasakian and equidistant hyperbolically Kählerian spaces.. Ukr. Geom. Sb. 32 (1989), 92–98. Zbl 0711.53042, MR 1049372 |
| Reference:
|
[21] Mikeš, J.: On Sasaki spaces and equidistant Kähler spaces.. Sov. Math., Dokl. 34 (1987), 428–431. Zbl 0631.53018, MR 0819428 |
| Reference:
|
[22] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces.. J. Math. Sci. 78, 3 (1996), 311–333. MR 1384327, 10.1007/BF02365193 |
| Reference:
|
[23] Mikeš, J.: On geodesic mappings of 2-Ricci symmetric Riemannian spaces.. Math. Notes 28 (1981), 622–624; Transl. from: Mat. Zametki 28 (1980), 313–317. MR 0587405, 10.1007/BF01157926 |
| Reference:
|
[24] Mikeš, J.: Geodesic mappings of $m$-symmetric and generalized semisymmetric spaces.. Russian Math. (Iz. VUZ) 36, 8 (1992), 38–42. MR 1233688 |
| Reference:
|
[25] Mikeš, J.: Geodesic mappings on semisymmetric spaces.. Russian Math. (Iz. VUZ) 38, 2 (1994), 35–41. MR 1302090 |
| Reference:
|
[26] Mikeš, J.: Equidistant Kähler spaces.. Math. Notes 38 (1985), 855–858. Zbl 0594.53024, MR 0819428, 10.1007/BF01158415 |
| Reference:
|
[27] Sekigawa, K.: Almost Hermitian manifolds satisfying some curvature conditions.. Kodai Math. J. 2 (1979), 384–405. Zbl 0423.53030, MR 0553243, 10.2996/kmj/1138036068 |
| Reference:
|
[28] Sharma, R.: Almost Ricci solitons and K-contact geometry.. Monatsh. Math. 175 (2014), 621–628. Zbl 1307.53038, MR 3273671, 10.1007/s00605-014-0657-8 |
| Reference:
|
[29] Sinyukov, N. S.: Geodesic Mappings of Riemannian Spaces.. Nauka, Moscow, 1979. Zbl 0637.53020 |
| Reference:
|
[30] Szabo, Z. I.: Structure theorems on Riemannian spaces satisfying $R(X,Y).R = 0$, The local version.. J. Diff. Geom. 17 (1982), 531–582. MR 0683165, 10.4310/jdg/1214437486 |
| Reference:
|
[31] Tripathi, M. M.: Ricci solitons in contact metric manifolds.. arXiv:0801,4222v1 [mathDG] 2008 (2008), 1–6. |
| Reference:
|
[32] Yadav, S., Suthar, D. L.: Certain derivation on Lorentzian $\alpha $-Sasakian manifold.. Global Journal of Science Frontier Research Mathematics and Decision Sciences 12, 2 (2012), 1–6. MR 2814463 |
| . |
