Beta-almost Ricci solitons on Sasakian 3-manifolds

• Autores: Pradip Majhi, Debabrata Kar
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 21, Nº. 3, 2019, págs. 63-74
• Idioma: inglés
• DOI: 10.4067/S0719-06462019000300063
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este artículo caracterizamos las 3-variedades Sasakianas que admiten solitones β-casi Ricci cuyo campo de vectores potencial es un campo de vectores de contacto. Entre otros, probamos que un solitón β-casi Ricci cuyo campo de vectores potencial es un campo de vectores de contacto en una 3-variedad Sasakiana se contrae, es Einstein y no trivial. Más aín, probamos que este tipo de variedades son isométricas a una esfera de radio √7.

  • English

    Abstract In this paper we characterize the Sasakian 3-manifolds admitting β-almost Ricci solitons whose potential vector field is a contact vector field. Among others we prove that a β-almost Ricci soliton whose potential vector field is a contact vector field on a Sasakian 3-manifold is shrinking, Einstein and non-trivial. Moreover, we prove that this type of manifolds are isometric to a sphere of radius √7.

• Referencias bibliográficas
  • Barros, A.,Ribeiro, Jr.. (2012). Some characterizations for compact almost Ricci solitons. Proc. Amer. Math. Soc.. 140.
  • Blair, D. E.. (1976). Lecture notes in Mathematics. Springer-Verlag. Berlin.
  • Blair, D. E.. (2002). Riemannian Geometry of contact and symplectic manifolds. Birkhäuser. Boston.
  • Blair, D. E.,Koufogiorgos, T.,Sharma, R.. (1990). A classification of 3-dimensional contact metric manifolds with Qφ = φQ. Kodai Math....
  • Calin, C.,Crasmareanu, M.. (2010). From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds. Bull. Malays. Math. Soc.. 33. 361
  • Chave, T.,Valent, G.. (1996). Quasi-Einstein metrics and their renoirmalizability properties. Helv. Phys. Acta.. 69. 344
  • Chave, T.,Valent, G.. (1996). On a class of compact and non-compact quasi-Einstein metrics and their renoirmalizability properties. Nuclear...
  • Deshmukh, S.. (2012). Jacobi-type vector fields on Ricci solitons. Bull. Math. Soc. Sci. Math. Roumanie. 55103. 41-50
  • Deshmukh, S.,Alodan, H.,Al-Sodais, H.. (2011). A Note on Ricci Soliton. Balkan J. Geom. Appl.. 16. 48-55
  • De, U. C.,Biswas, S.. (2006). A note on ξ-conformally flat contact manifolds. Bull. Malays. Math. Soc.. 29. 51
  • De, U. C.,Mondal, A. K.. (2012). Three dimensional Quasi-Sasakian manifolds and Ricci solitons,. SUT J. Math.. 48. 71-81
  • De, U. C.,Mondal, A. K.. (2013). The structure of some classes of 3-dimensional normal almost contact metric manifolds. Bull. Malays. Math....
  • De, Avik,Jun, J. B.. (2011). On N(k)-contact metric manifolds satisfying certain curvature conditions. Kyungpook Math. J.. 51. 457
  • Friedan, D.. (1985). Nonlinear models in 2 + ∊ dimensions. Ann. Phys.. 163. 318-419
  • Ghosh, A.,Sharma, R.. (2014). Sasakian metric as a Ricci soliton and related results. J. Geom. Phys.. 75. 1-6
  • Ghosh, A.,Patra, D. S.. (2018). The k-almost Ricci solitons and contact geometry. J. Korean. Math.. 55. 161
  • Hamilton, R. S.. (1988). Mathematics and general relativity. American Math. Soc..
  • Hamilton, R. S.. (1982). Three manifolds with positive Ricci curvature. J. Differential Geom.. 17. 255-306
  • Ivey, T.. (1993). Ricci solitons on compact 3-manifolds. Diff. Geom. Appl.. 3. 301
  • Kim, B.H.. (1990). Fibered Riemannian spaces with quasi-Sasakian structures. Hiroshima Math. J.. 20. 477-513
  • Majhi, P.,De, U. C.. (2015). Classifications of N(k)-contact metric manifolds satisfying certain curvature conditions. Acta Math. Univ. Commenianae....
  • Özgür, C.. (2002). Contact metric manifolds with cyclic-parallel Ricci tensor. Diff. Geom. Dynamical systems. 4. 21
  • Özgür, C.,Sular, S.. (2008). On N(k)-contact metric manifolds satisfying certain conditions. SUT J. Math.. 44. 89-99
  • Pigola, S.,Rigoli, M.,Rimoldi, M.,Setti, A.. (2011). Ricci almost solitons. Ann. Sc. Norm. Super.Pisa Cl. Sci,. 510. 757
  • Taleshian, A.,Hosseinzabeh, A. A.. (2011). Investigation of Some Conditions on N(k)-Quasi Einstein Manifolds. Bull. Malays. Math. Soc.. 34....
  • Gomes, J. N.,Wang, Q.,Xia, C.. (2017). On the h-almost Ricci soliton. J. Geom. Phys.. 114. 216
  • Wang, Y.,Liu, X.. (2015). Ricci solitons on three-dimensional η-Einstein almost Kenmotsu man-ifolds. Taiwanese Journal of Mathematics. 19....
  • Wang, Y.. (2017). Ricci solitons on 3-dimensional cosympletic manifolds. Math. Slovaca. 67. 979