Year 2022,
Volume: 51 Issue: 6, 1535 - 1549, 01.12.2022
Mohd Aquib
,
Siraj Uddin
,
M. Hasan Shahid
References
- [1] P. Alegre, D.E. Blair and A. Carriazo, Generalized Sasakian space forms, Israel J.
Math. 141, 157–183, 2004.
- [2] P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Differ.
Geom. Appl. 26 (6), 656–666, 2008.
- [3] P. Alegre and A. Carriazo, Submanifolds of generalized Sasakian space forms, Taiwan.
J. Math. 13, 923–941, 2009.
- [4] P. Alegre and A. Carriazo, Generalized Sasakian space forms and conformal changes
of the metric, Results Math. 59, 485–493, 2011.
- [5] R. Al-Ghefari, F.R. Al-Solamy and M.H. Shahid, CR-submanifolds of generalized
Sasakian space-forms, JP J. Geom. Topol. 6, 151–166, 2006.
- [6] M. Aquib, M.N. Boyom, M.H. Shahid and G. Vîlcu, The first fundamental equation
and generalized wintgen-type inequalities for submanifolds in generalized space forms,
Mathematics, 7, (2019) 1151. doi:10.3390/math7121151.
- [7] M. Atçeken , Contact CR-warped product submanifolds in Sasakian space forms,
Hacet. J. Math. Stat. 44 (1), 23–32, 2015.
- [8] R.L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math.
Soc. 145, 1–49, 1967.
- [9] B.Y. Chen, On isometric minimal immersions from warped products into real space
forms, Proc. Edinb. Math. Soc. 45, 579–587, 2002.
- [10] B.Y. Chen, Geometry of warped products as Riemannian submanifolds and related
problem, Soochow J. Math. 28, 125–157, 2002.
- [11] B.Y. Chen, CR-warped products in complex projective spaces with compact holomorphic
factor, Monatsh. Math. 141 (3), 177–186, 2004.
- [12] B.Y. Chen, Geometry of warped product submanifolds: a survey, J. Adv. Math. Stud.
6 (2), 1–43, 2013.
- [13] B.Y. Chen, Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific,
2011.
- [14] A. Mustafa, A. De and S. Uddin, Characterization of warped product submanifolds in
Kenmotsu manifolds, Balkan. J. Geom. Appl. 20, 86–97, 2015.
- [15] M. Falcitelli, Locally conformal C6-manifolds and generalized Sasakian-space-forms,
Mediterr. J. Math. 7, 19–36, 2010.
- [16] S.K. Hui, S. Uddin, A. Alkhaldi and P. Mandal, Invariant submanifolds of generalized
Sasakian-space-forms, Int. J. Geom. Methods Mod. Phys. 15 (9), 2018.
- [17] U.K. Kim, Conformally flat generalized Sasakian-space-forms and locally symmetric
generalized Sasakian-space-forms, Note Mat. 26, 55–67, 2006.
- [18] F. Malek and V. Nejadakbary, A lower bound for the Ricci curvature of submanifolds
in generalized Sasakian space forms, Adv. Geom. 13, 695–711, 2013.
- [19] M.I. Munteanu, Warped product contact CR-submanifolds of Sasakian space forms,
Publ. Math. Debrecen, 66, 75–120, 2005.
- [20] C. Ozgur and S. Guvenc, On some classes of biharmonic Legendre curves in generalized
Sasakian space forms, Collect. Math. 65, 203–218, 2014.
- [21] S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped product bi-slant immersions in
Kaehler manifolds, Mediterr. J. Math. 14 (2), (2017) 11.
- [22] S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant immersions in Sasakian
manifolds, Publ.Math. Debrecen 91 ((3-4)), 331–348 2017.
Ricci curvature for pointwise semi-slant warped products in non-Sasakian generalized Sasakian space forms and its applications
Year 2022,
Volume: 51 Issue: 6, 1535 - 1549, 01.12.2022
Mohd Aquib
,
Siraj Uddin
,
M. Hasan Shahid
Abstract
We find Ricci curvature bounds for pointwise semi-slant warped products submanifolds in non-Sasakian generalized Sasakian space forms in this work, and analyze the equality case of the inequality. The derived inequality is also used to develop a number of applications.
References
- [1] P. Alegre, D.E. Blair and A. Carriazo, Generalized Sasakian space forms, Israel J.
Math. 141, 157–183, 2004.
- [2] P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Differ.
Geom. Appl. 26 (6), 656–666, 2008.
- [3] P. Alegre and A. Carriazo, Submanifolds of generalized Sasakian space forms, Taiwan.
J. Math. 13, 923–941, 2009.
- [4] P. Alegre and A. Carriazo, Generalized Sasakian space forms and conformal changes
of the metric, Results Math. 59, 485–493, 2011.
- [5] R. Al-Ghefari, F.R. Al-Solamy and M.H. Shahid, CR-submanifolds of generalized
Sasakian space-forms, JP J. Geom. Topol. 6, 151–166, 2006.
- [6] M. Aquib, M.N. Boyom, M.H. Shahid and G. Vîlcu, The first fundamental equation
and generalized wintgen-type inequalities for submanifolds in generalized space forms,
Mathematics, 7, (2019) 1151. doi:10.3390/math7121151.
- [7] M. Atçeken , Contact CR-warped product submanifolds in Sasakian space forms,
Hacet. J. Math. Stat. 44 (1), 23–32, 2015.
- [8] R.L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math.
Soc. 145, 1–49, 1967.
- [9] B.Y. Chen, On isometric minimal immersions from warped products into real space
forms, Proc. Edinb. Math. Soc. 45, 579–587, 2002.
- [10] B.Y. Chen, Geometry of warped products as Riemannian submanifolds and related
problem, Soochow J. Math. 28, 125–157, 2002.
- [11] B.Y. Chen, CR-warped products in complex projective spaces with compact holomorphic
factor, Monatsh. Math. 141 (3), 177–186, 2004.
- [12] B.Y. Chen, Geometry of warped product submanifolds: a survey, J. Adv. Math. Stud.
6 (2), 1–43, 2013.
- [13] B.Y. Chen, Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific,
2011.
- [14] A. Mustafa, A. De and S. Uddin, Characterization of warped product submanifolds in
Kenmotsu manifolds, Balkan. J. Geom. Appl. 20, 86–97, 2015.
- [15] M. Falcitelli, Locally conformal C6-manifolds and generalized Sasakian-space-forms,
Mediterr. J. Math. 7, 19–36, 2010.
- [16] S.K. Hui, S. Uddin, A. Alkhaldi and P. Mandal, Invariant submanifolds of generalized
Sasakian-space-forms, Int. J. Geom. Methods Mod. Phys. 15 (9), 2018.
- [17] U.K. Kim, Conformally flat generalized Sasakian-space-forms and locally symmetric
generalized Sasakian-space-forms, Note Mat. 26, 55–67, 2006.
- [18] F. Malek and V. Nejadakbary, A lower bound for the Ricci curvature of submanifolds
in generalized Sasakian space forms, Adv. Geom. 13, 695–711, 2013.
- [19] M.I. Munteanu, Warped product contact CR-submanifolds of Sasakian space forms,
Publ. Math. Debrecen, 66, 75–120, 2005.
- [20] C. Ozgur and S. Guvenc, On some classes of biharmonic Legendre curves in generalized
Sasakian space forms, Collect. Math. 65, 203–218, 2014.
- [21] S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped product bi-slant immersions in
Kaehler manifolds, Mediterr. J. Math. 14 (2), (2017) 11.
- [22] S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant immersions in Sasakian
manifolds, Publ.Math. Debrecen 91 ((3-4)), 331–348 2017.