757
Views
3
CrossRef citations to date
0
Altmetric
Research Articles

Chen optimal inequalities of CR-warped products of generalized Sasakian space form

ORCID Icon, ORCID Icon & ORCID Icon
Pages 322-330 | Received 16 Sep 2019, Accepted 23 Feb 2020, Published online: 13 Mar 2020

References

  • Chen BY. An optimal inequality for CR-warped products in complex space forms involving CR δ-invariant. Int J Math. 2012;23(3).
  • Al-Solamy F, Chen BY, Deshmukh S. Two optimal inequalities for anti-holomorphic submanifolds and their applications. Taiwanese J Math. 2014;18:199–217. doi: 10.11650/tjm.18.2014.3241
  • Al-Solamy F, Chen BY, Deshmukh S. Erratum to: Two optimal inequalities for anti-holomorphic submanifolds and their applications. Taiwanese J Math. 2018;22(3):615–616. doi: 10.11650/tjm/180405
  • Mihai I, Presură I. An inequality for contact CR-submanifolds in Sasakian space forms. J Geom. 2018;109(2):34. doi: 10.1007/s00022-018-0440-4
  • Kenmotsu K. A class of almost contact Riemannian manifolds. Tohoku Math J. 1972;24:93–103. doi: 10.2748/tmj/1178241594
  • Blair DE. Contact manifolds in Riemannian geometry. Springer Verlag. (1976). (Lecture Notes in Mathematics; 509.
  • Ludden GD. Submanifolds of cosymplectic manifolds. J Diff Geom. 1970;4:237–244. doi: 10.4310/jdg/1214429387
  • Oubina JA. New classes of almost contact metric structures. Publ Math Debrecen. 1985;32:187–193.
  • Gray A, Hervella LM. The sixteen classes of almost Hermitian manifolds and their linear invariants. Ann Mat Pura Appl. 1980;123:35–58. doi: 10.1007/BF01796539
  • Alegre P, Blair DE, Carriazo A. Generalized Sasakian space forms. Israel J Math. 2004;141:157–183. doi: 10.1007/BF02772217
  • Yano K, Kon M. Structures on manifolds. Singapore: Worlds Scientific; 1984.
  • Yano K, Kon M. Generic submanifolds of Sasakian manifolds. Kodai Math J. 1980;3:163–196. doi: 10.2996/kmj/1138036191
  • Bishop RL, O'Neill B. Manifolds of negative curvature. Trans Amer Math Soc. 1969;145:1–49. doi: 10.1090/S0002-9947-1969-0251664-4
  • Chen BY. Differential geometry of warped product manifolds and submanifolds. Hackensack, NJ: Worlds Scientific; 2017.
  • Hasegawa I, Mihai I. Contact CR-warped product submanifolds in Sasakian manifolds. Geom Dedicata. 2003;102:143–150. doi: 10.1023/B:GEOM.0000006582.29685.22
  • Chen BY. Geometry of warped product CR-submanifolds in Kaehler manifold. Monatsh Math. 2001;133:177–195. doi: 10.1007/s006050170019
  • Chen BY. Geometry of warped product CR-submanifolds in Kaehler manifolds II. Monatsh Math. 2001;134:103–119. doi: 10.1007/s006050170002
  • Sular SOzgur C. Contact CR-warped product submanifolds in generalized Sasakian space forms. Turk J Math. 2012;36:485–497.
  • Chen BY. δ-Invariants, Inequalities of Submanifolds and Their Applications. (2013); arXiv preprint arXiv:1307.1877
  • Ali A, Laurian-Ioan P. Geometric classification of warped products isometrically immersed in Sasakian space forms. Math Nachr. 2018;292:234–251.
  • Ali A, Luarian P. Geometry of warped product immersions of Kenmotsu space forms and its applications to slant immersions. J Geom Phys. 2017;114:276–290. doi: 10.1016/j.geomphys.2016.12.001
  • Ali A, Ozel C. Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications. Int J Geom. Meth. Mod. Phys. 2017;14(3):1750042. doi: 10.1142/S0219887817500426
  • Baishya KK, Nurcan F, Jana SK. On the existence of an almost generalized weakly-symmetric Sasakian manifold admitting quarter symmetric metric connection. J Taibah Univ Sci. 2019;13(1):941–946. doi: 10.1080/16583655.2019.1663033
  • Abu-Saleem M. Folding on manifolds and their fundamental group. J Taibah Univ Sci. 2019;13(1):16–19. doi: 10.1080/16583655.2018.1516396
  • Yldrm Ü, Atceken M, Dirik S. B Y Chen inequalites for semi-slant submanifolds in normal paracontact metric manifolds. Palestine J Math. 2018;7(1):281–288.