Geometric inequalities for doubly warped products pointwise bi-slant submanifolds in conformal Sasakian space form. (English) Zbl 1513.53041
Summary: In this paper, we have established some geometric inequalities for the squared mean curvature in terms of warping functions of a doubly warped product pointwise bi-slant submanifold of a conformal Sasakian space form with a quarter symmetric metric connection. The equality cases havve also been considered. Moreover, some applications of obtained results are derived.
MSC:
| 53B25 | Local submanifolds |
| 53C40 | Global submanifolds |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
Keywords:
doubly warped products; bi-slant submanifolds; metric connection; conformal Sasakian space formReferences:
| [1] | 1.E. Abedi, R. Bahrami, M. M. Tirpathi:Ricci and Scalar curvatures of submanifolds of a conformal Sasakian space form, Archivum Mathematicum (BRNO) Tomus52(2016), 113-130. · Zbl 1374.53082 |
| [2] | 2.R. L. BishopandB. O’Neil:Manifolds of negative curvature, Trans. Amer. Math. Soc.145(1969), 1-9. · Zbl 0191.52002 |
| [3] | 3.D. E. Blair:Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics,509. Springer-Verlag, New York, (1976). · Zbl 0319.53026 |
| [4] | 4.B. Y. Chen:Geometry of warped product CR-submanifold in Kaehler manifolds, Monatsh. Math.133(3) (2001), 177-195. · Zbl 0996.53044 |
| [5] | 5.B. Chen:On isometric minimal immersion from warped product submanifolds into real space forms, Proc. Edinburgh Math. Soc. (2002), 579-587. · Zbl 1022.53022 |
| [6] | 6.B.-Y. Chen, O. J. Gray:Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math.79(2012), 630-640. · Zbl 1269.53059 |
| [7] | 7.B.-Y. Chen:Pseudo-Riemannian geometry,δ-invariants and applications, World Scientific, Hackensack, NJ, (2011). · Zbl 1245.53001 |
| [8] | 8.B.-Y. Chen, S. UddinWarped product pointwise bi-slant submanifolds of Kaehler manifolds, Publ. Math. Debrecen (1-2)92(2018), 183-199. · Zbl 1413.53101 |
| [9] | 9.M. A. Khan, K.Khan:Bi-warped product submanifolds of complex space forms, International Journal of Geometric methods in Modern Physics,16, 05, (2019). · Zbl 1422.53044 |
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