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Keywords:
Conformal Ricci soliton; conformal curvature tensor; conharmonic curvature tensor; Lorentzian $\alpha $-Sasakian manifolds; projective curvature tensor
Conformal Ricci soliton; conformal curvature tensor; conharmonic curvature tensor; Lorentzian $\alpha $-Sasakian manifolds; projective curvature tensor
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.
References:
[1] Bagewadi, C. S., Ingalahalli, G.: Ricci solitons in Lorentzian $\alpha $-Sasakian manifolds. Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 28 (2012), 59–68. MR 2942704 | Zbl 1265.53036
[2] Bagewadi, C. S., :, Venkatesha: Some curvature tensors on a trans-Sasakian manifold. Turk. J. Math. 31 (2007), 111–121. MR 2335656 | Zbl 1138.53028
[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
[4] Bejan, C. L., Crasmareanu, M.: Ricci solitons in manifolds with quasi-constant curvature. Publ. Math. Debrecen 78, 1 (2011), 235–243. DOI 10.5486/PMD.2011.4797 | MR 2777674 | Zbl 1274.53097
[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. DOI 10.1080/1726037X.2015.1076221 | MR 3427160
[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. MR 3699549 | Zbl 1369.53021
[7] Dutta, T., Bhattacharyya, A., Debnath, S.: Conformal Ricci soliton in almost C($\lambda $) manifold. Internat. J. Math. Combin. 3 (2016), 17–26.
[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. MR 2783789 | Zbl 1207.53040
[9] Fischer, A. E.: An introduction to conformal Ricci flow. class.Quantum Grav. 21 (2004), S171–S218. DOI 10.1088/0264-9381/21/3/011 | MR 2053005 | Zbl 1050.53029
[10] Formella, S., Mikeš, J.: Geodesic mappings of Einstein spaces. Ann. Sci. Stetinenses 9 (1994), 31–40.
[11] Hamilton, R. S.: Three Manifold with positive Ricci curvature. J. Differential Geom. 17, 2 (1982), 255–306. DOI 10.4310/jdg/1214436922 | MR 0664497
[12] Hamilton, R. S.: The Ricci flow on surfaces. Contemporary Mathematics 71 (1988), 237–261. DOI 10.1090/conm/071/954419 | MR 0954419 | Zbl 0663.53031
[13] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces. In: Geometric Methods in Physics, Trends in Mathematics, Birkhäuser, Basel, 2013, 331–335. MR 3364052 | Zbl 1268.53049
[14] Hinterleitner, I., Kiosak, V.: $\varphi (Ric)$-vektor fields in Riemannian spaces. Arch. Math. 5 (2008), 385–390. MR 2501574
[15] Hinterleitner, I., Kiosak, V.: $\varphi (Ric)$-vector fields on conformally flat spaces. AIP Conf. Proc. 1191 (2009), 98–103.
[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.
[17] Mikeš, J.: Geodesic mappings of semisymmetric Riemannian spaces. Archives at VINITI, Odessk. Univ., Moscow, 1976.
[18] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations. Palacky Univ. Press, Olomouc, 2009. MR 2682926 | Zbl 1222.53002
[19] Mikeš, J.: Differential Geometry of Special Mappings. Palacky Univ. Press, Olomouc, 2015. MR 3442960 | Zbl 1337.53001
[20] Mikeš, J., Starko, G. A.: On hyperbolically Sasakian and equidistant hyperbolically Kählerian spaces. Ukr. Geom. Sb. 32 (1989), 92–98. MR 1049372 | Zbl 0711.53042
[21] Mikeš, J.: On Sasaki spaces and equidistant Kähler spaces. Sov. Math., Dokl. 34 (1987), 428–431. MR 0819428 | Zbl 0631.53018
[22] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci. 78, 3 (1996), 311–333. DOI 10.1007/BF02365193 | MR 1384327
[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. DOI 10.1007/BF01157926 | MR 0587405
[24] Mikeš, J.: Geodesic mappings of $m$-symmetric and generalized semisymmetric spaces. Russian Math. (Iz. VUZ) 36, 8 (1992), 38–42. MR 1233688
[25] Mikeš, J.: Geodesic mappings on semisymmetric spaces. Russian Math. (Iz. VUZ) 38, 2 (1994), 35–41. MR 1302090
[26] Mikeš, J.: Equidistant Kähler spaces. Math. Notes 38 (1985), 855–858. DOI 10.1007/BF01158415 | MR 0819428 | Zbl 0594.53024
[27] Sekigawa, K.: Almost Hermitian manifolds satisfying some curvature conditions. Kodai Math. J. 2 (1979), 384–405. DOI 10.2996/kmj/1138036068 | MR 0553243 | Zbl 0423.53030
[28] Sharma, R.: Almost Ricci solitons and K-contact geometry. Monatsh. Math. 175 (2014), 621–628. DOI 10.1007/s00605-014-0657-8 | MR 3273671 | Zbl 1307.53038
[29] Sinyukov, N. S.: Geodesic Mappings of Riemannian Spaces. Nauka, Moscow, 1979. Zbl 0637.53020
[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. DOI 10.4310/jdg/1214437486 | MR 0683165
[31] Tripathi, M. M.: Ricci solitons in contact metric manifolds. arXiv:0801,4222v1 [mathDG] 2008 (2008), 1–6.
[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
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