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Yamabe Solitons and Ricci Solitons on Almost co-Kähler Manifolds

  • Young Jin Suh (a1) and Uday Chand De (a2)

Abstract

The object of this paper is to study Yamabe solitons on almost co-Kähler manifolds as well as on $(k,\unicode[STIX]{x1D707})$ -almost co-Kähler manifolds. We also study Ricci solitons on $(k,\unicode[STIX]{x1D707})$ -almost co-Kähler manifolds.

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The first author was supported by the National Research Foundation of Korea, Grant Proj. No. NRF-2018-R1D1A1B-05040381.

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[1] Bejan, C. L. and Crasmareanu, M., Ricci solitons in manifolds with quasi-constant curvature . Publ. Math. Debrecen 78(2011), 235243. https://doi.org/10.5486/PMD.2011.4797.
[2] Blair, D. E., Contact manifold in Riemannian geometry. Lecture Notes in Mathematics, 509, Springer-Verlag, Berlin, 1976.
[3] Blair, D. E., Riemannian geometry on contact and symplectic manifolds. Progress in Mathematics, 203, Birkhäuser Boston, Inc, Boston, MA, 2002. https://doi.org/10.1007/978-1-4757-3604-5.
[4] Calin, C. and Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds . Bull. Malays. Math. Sci. Soc. 33(2010), 361368.
[5] Cappelletti-Montano, B., Nicola, A. D., and Yudin, I., A survey on cosymplectic geometry . Rev. Math. Phys. 25(2013), 1343002 (2013). https://doi.org/10.1142/S0129055X13430022.
[6] Cappelletti-Montano, B. and Pastore, A. M., Einstein-like conditions and cosymplectic geometry . J. Adv. Math. Stud. 3(2010), 2740.
[7] Carriazo, A. and Martin-Molina, V., Almost cosymplectic and almost Kenmotsu (k, 𝜇, 𝜈)-spaces . Mediterr. J. Math. 10(2013), 15511571. https://doi.org/10.1007/s00009-013-0246-4.
[8] Chave, T. and Valent, G., Quasi-Einstein metrics and their renoirmalizability properties . Helv. Phys. Acta. 69(1996), 344347.
[9] Chave, T. and Valent, G., On a class of compact and non-compact quasi-Einstein metrics and their renoirmalizability properties . Nuclear Phys. B. 478(1996), 758778. https://doi.org/10.1016/0550-3213(96)00341-0.
[10] Chinea, D., de Leon, M., and Marrero, J. C., Topology of cosymplectic manifolds . J. Math. Pures Appl. 72(1993), 567591.
[11] Cho, J. T., Ricci solitons on almost contact geometry. Proceedings of 17th International workshop on Differential Geometry and the 7th KNUGRG-OCAMI Differential Geometry Workshop [Vol. 17], Natl. Inst. Math. Sci. (NIMS), Taejon, 2013, pp. 8595.
[12] Chow, B. and Knopf, D., The Ricci flow: An introduction. Mathematical Surveys and Monographs, 110, American Mathematical Society, Providence, RI, 2004.
[13] Chow, B., Lu, P., and Ni, L., Hamilton Ricci flow. Graduate Studies in Mathematics, 77, American Mathematical Society, Providence, RI; Science Press, Beijing, New York, 2006. https://doi.org/10.1090/gsm/077.
[14] Dacko, P. and Olszak, Z., On almost cosymplectic (k, 𝜇)-space. Banach Center Publ. 69, Polish Acad. Sci. Inst. Math., Warsaw, 2005, pp. 211220. https://doi.org/10.4064/bc69-0-17.
[15] Daskalopoulos, P. and Sesum, N., The classification of locally conformally flat Yamabe solitons . Adv. Math. 240(2013), 346369. https://doi.org/10.1016/j.aim.2013.03.011.
[16] Derdzinski, A., A., Compact Ricci solitons . (Polish) Wiad Mat. 48(2012), no. 1, 132.
[17] Deshmukh, S., Jacobi-type vector fields on Ricci solitons . Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(2012), 4150.
[18] Endo, H., Non-existence of almost cosymplectic manifolds satisfying a certain condition . Tensor (N. S.) 63(2002), 272284.
[19] Hamilton, R. S., The Ricci flow on surfaces . In: Mathematics and general relativity, Contemp. Math., 71, American Mathematica Society, Providence, RI, 1988, pp. 237262. https://doi.org/10.1090/conm/071/954419.
[20] Hsu, S.-Y., A note on compact gradient Yamabe solitons . J. Math. Anal. Appl. 388(2012), 725726. https://doi.org/10.1016/j.jmaa.2011.09.062.
[21] Ivey, T., Ricci solitons on compact 3-manifolds . Differential Geom. Appl. 3(1993), 301307. https://doi.org/10.1016/0926-2245(93)90008-O.
[22] Jun, J. B. and Kim, U. K., On 3-dimentional almost contact metric manifold . Kyungpook Math. J. 34(1994), 293301.
[23] Li, H., H., Topology of co-symplectic/co-Kähler manifolds . Asian J. Math. 12(2008), 527543. https://doi.org/10.4310/AJM.2008.v12.n4.a7.
[24] Marrero, J. C. and Padron, E., New examples of compact cosymplectic solvmanifolds . Arch. Math. (Brno) 34(1998), 337345.
[25] Olszak, Z., On almost cosymplectic manifolds . Kodai Math. J. 4(1981), 239250.
[26] Olszak, Z., On almost cosymplectic manifolds with Kählerian leaves . Tensor (N. S.) 46(1987), 117124.
[27]H. Oztürk, H., N. Aktan, C. and Murathan, Almost 𝛼-cosymplectic (k, 𝜇, 𝜈)-spaces. 2010. arxiv:1007.0527v1.
[28] Perelman, G., The entropy formula for the Ricci flow and its geometric applications. arxiv:Math.DG/0211159.
[29] Sharma, R., A 3-dimensional Sasakian metric as a Yamabe Soliton . Int. J. Geom. Methods Mod. Phys. 9(2012), 1220003. https://doi.org/10.1142/S0219887812200034.
[30] Wang, Y., Yamabe solitons in three dimensional Kenmotsu manifolds . Bull. Belg. Math. Soc. Stenvin 23(2016), 345355.
[31] Wang, Y., A generalization of Goldberg conjecture for co-Kähler manifolds . Mediterr. J. Math. 13(2016), 26792690.
[32] Yano, K., Integral Formulas in Riemannian geometry. Pure and Applied Mathematics, 1, Marcel Dekker, New York, 1970.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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