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Articles

Ricci η-parallel trans-Sasakian 3-manifolds

Pages 7-15 | Received 10 Jun 2019, Published online: 07 Nov 2019

References

  • D.E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, Vol. 203, Birkhäuser, Basel, 2010.
  • D. Chinea and C. Gonzalez, A classification of almost contact metric manifolds, Ann. Mat. Pura Appl. 156 (1990), 15–36. doi: 10.1007/BF01766972
  • J.T. Cho, η-parallel contact 3-manifolds, Bull. Korean Math. Soc. 46, (2009), 577– 589. doi: 10.4134/BKMS.2009.46.3.577
  • J.T. Cho, η-parallel H contact 3-manifolds, Bull. Korean Math. Soc. 55 (2018), 1013–1022.
  • U.C. De and K. De, On a class of three-dimensional trans-Sasakian manifolds, Commun. Korean Math. Soc. 27 (2012), 795–808. doi: 10.4134/CKMS.2012.27.4.795
  • U.C. De and A.K. Mondal, On 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions, Commun. Korean Math. Soc. 24 (2009), 265–275. doi: 10.4134/CKMS.2009.24.2.265
  • U.C. De and A.K. Mondal, The structure of some classes of 3-dimensional normal almost contact metric manifolds, Bull. Malays. Math. Sci. Soc. 36 (2013), 501–509.
  • U.C. De and A. Sarkar, On three-dimensional trans-Sasakian manifolds, Extracta Math. 23 (2008), 265–277.
  • U.C. De and M.M. Tripathi, Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math. J. 43 (2003), 247–255.
  • S. Deshmukh, Trans-Sasakian manifolds homothetic to Sasakian manifolds, Mediterr. J. Math. 13 (2016), 2951–2958. doi: 10.1007/s00009-015-0666-4
  • S. Deshmukh, Geometry of 3-dimensional trans-Sasakaian manifolds, An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.) 63 (2016), 183–192.
  • S. Deshmukh and F. Al-Solamy, A Note on compact trans-Sasakian manifolds, Mediterr. J. Math. 13 (2016), 2099–2104. doi: 10.1007/s00009-015-0582-7
  • S. Deshmukh and M.M. Tripathi, A Note on compact trans-Sasakian manifolds, Math. Slovaca 63 (2013), 1361–1370. doi: 10.2478/s12175-013-0176-4
  • J. Inoguchi, A note on almost contact Riemannian 3-manifolds II, Bull. Korean Math. Soc. 54 (2017), 85–97. doi: 10.4134/BKMS.b150772
  • D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), 1–27. doi: 10.2996/kmj/1138036310
  • J.C. Marrero, The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl. 162 (1992), 77–86. doi: 10.1007/BF01760000
  • K. Okumura, Certain almost contact hypersurfaces in Kaehlerian manifolds of constant holomorphic sectional curvatures, Tohoku Math. J. 16 (1964), 270–284. doi: 10.2748/tmj/1178243673
  • Z. Olszak, Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. 47 (1986), 41–50. doi: 10.4064/ap-47-1-41-50
  • Z. Olszak and R. Rosca, Normal locally conformal almost cosymplectic manifolds, Publ. Math. Debrecen 39 (1991), 315–323.
  • A. Oubiña, New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), 187–193.
  • W. Wang and X. Liu, Ricci tensors on trans-Sasakian 3-manifolds, Filomat 32 (2018), 4365–4374. doi: 10.2298/FIL1812365W
  • Y. Wang, Ricci tensors on three-dimensional almost coKähler manifolds, Kodai Math. J. 39 (2016), 469–483. doi: 10.2996/kmj/1478073764
  • Y. Wang, Three-dimensional almost Kenmotsu manifolds with η-parallel Ricci tensor, J. Korean Math. Soc. 54 (2017), 793–805. doi: 10.4134/JKMS.j160252
  • Y. Wang, Minimal and harmonic Reeb vector fields on trans-Sasakian 3-manifolds, J. Korean Math. Soc. 55 (2018), 1321–1336.
  • Y. Wang and W. Wang, A remark on trans-Sasakian 3-manifolds, Rev. Union Mat. Argentina 60 (2019), 257–264. doi: 10.33044/revuma.v60n1a16
  • A. Yildiz, U.C. De, and M. Turan, On 3-dimensional f -Kenmotsu manifolds and Ricci solitons, Ukrainian Math. J. 65 (2013), 684–693. doi: 10.1007/s11253-013-0806-6

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