Eta-Ricci solitons on LP-Sasakian manifolds

• Autores: Pradip Majhi, Debabrata Kar
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 2, 2019, págs. 391-405
• Idioma: inglés
• DOI: 10.33044/revuma.v60n2a07
• Enlaces
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• Resumen

  • We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds with Codazzi type of the Ricci tensor. Then we study η-Ricci solitons on ϕ-conformally semi-symmetric, ϕ-Ricci symmetric, and conformally Ricci semi-symmetric Lorentzian para-Sasakian manifolds. Finally, we construct an example of a three dimensional Lorentzian para-Sasakian manifold which admits η-Ricci solitons with non-constant scalar curvature.

• Referencias bibliográficas
  • Batat, W., Brozos-V´azquez, M., Garc´ıa-R´ıo, E. and Gavino-Fern´andez, S., Ricci solitons on Lorentzian manifolds with large isometry groups,...
  • Blaga, A. M., Eta-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl. 20 (2015), no. 1, 1–13. MR 3367062.
  • Blaga, A. M., η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat 30 (2016), no. 2, 489–496. MR 3497930.
  • Boeckx, E., Kowalski, O. and Vanhecke, L., Riemannian manifolds of conullity two, World Scientific Publishing, 1996. MR 1462887.
  • Brozos-V´azquez, M., Calvaruso, G., Garc´ıa-R´ıo, E. and Gavino-Fern´andez, S., Threedimensional Lorentzian homogeneous Ricci solitons, Israel...
  • C˘alin, C. and Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bull. Malays. Math. Sci. Soc. 33 (2010),...
  • Cartan, E., Sur une classe remarquable d’espaces de Riemann, Bull. Soc. Math. France 54 (1926), 214–264. MR 1504900.
  • Chave, T. and Valent, G., Quasi-Einstein metrics and their renormalizability properties, Helv. Phys. Acta 69 (1996), no. 3, 344–347. MR 1440692.
  • Chave, T. and Valent, G., On a class of compact and non-compact quasi-Einstein metrics and their renormalizability properties, Nuclear Phys....
  • Chern, S. S., What is geometry?, Amer. Math. Monthly 97 (1990), no. 8, 679–686 MR 1072811.
  • Cho, J. T. and Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. 61 (2009), no. 2, 205–212. MR 2541405.
  • De, K. and De, U. C., LP-Sasakian manifolds with quasi-conformal curvature tensor, SUT J. Math. 49 (2013), no. 1, 33–46. MR 3135226.
  • De, U. C. and Sarkar, A., On ϕ-Ricci symmetric Sasakian manifolds, Proc. Jangjeon Math. Soc. 11 (2008), no. 1, 47–52. MR 2429328.
  • Deshmukh, S., Jacobi-type vector fields on Ricci solitons, Bull. Math. Soc. Sci. Math. Roumanie 55(103) (2012), no. 1, 41–50. MR 2951970.
  • Deshmukh, S., Alodan, H. and Al-Sodais, H., A note on Ricci solitons, Balkan J. Geom. Appl. 16 (2011), no. 1, 48–55. MR 2785715.
  • Friedan, D. H., Nonlinear models in 2+ε dimensions, Ann. Phys. 163 (1985), no. 2, 318–419. MR 0811072.
  • Gray, A., Einstein-like manifolds which are not Einstein, Geom. Dedicata 7 (1978), no. 3, 259–280. MR 0505561.
  • Hamilton, R. S., The Ricci flow on surfaces, In: Mathematics and general relativity (Santa Cruz, CA, 1986), 237–262. Contemp. Math., 71, Amer....
  • Ivey, T., Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993), no. 4, 301–307. MR 1249376.
  • Kowalski, O., An explicit classification of 3-dimensional Riemannian spaces satisfying R(X, Y ) · R = 0, Czechoslovak Math. J. 46(121)...
  • Matsumoto, K., On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci. 12 (1989), no. 2, 151–156. MR 0994289.
  • Matsumoto, K., Mihai, I. and Ro¸sca, R., ξ-null geodesic gradient vector fields on a Lorentzian para-Sasakian manifold, J. Korean Math. Soc....
  • Onda, K., Lorentz Ricci solitons on 3-dimensional Lie groups, Geom. Dedicata 147 (2010), 313–322. MR 2660582.
  • Ozg¨ur, C., ¨ ϕ-conformally flat Lorentzian para-Sasakian manifolds, Rad. Mat. 12 (2003), no. 1, 99–106. MR 2022248.
  • Prakasha, D. G. and Hadimani, B. S., η-Ricci solitons on para-Sasakian manifolds, J. Geom. 108 (2017), no. 2, 383–392. MR 3667227
  • Szab´o, Z. I., Structure theorems on Riemannian spaces satisfying R(X, Y ) · R = 0. I. The local version, J. Differential Geom. 17 (1982),...
  • Taleshian, A. and Asghari, N., On LP-Sasakian manifolds satisfying certain conditions on the concircular curvature tensor, Differ. Geom. Dyn....
  • Verstraelen, L., Comments on pseudo-symmetry in the sense of Ryszard Deszcz, In: Geometry and topology of submanifolds, VI (Leuven, 1993/Brussels,...
  • Yildiz, A. and De, U. C., A classification of (k, µ)-contact metric manifolds, Commun. Korean Math. Soc. 27 (2012), no. 2, 327–339. MR 2962526.