### GEOMETRIC INEQUALITIES FOR DOUBLY WARPED PRODUCTS POINTWISE BI-SLANT SUBMANIFOLDS IN CONFORMAL SASAKIAN SPACE FORM

**DOI Number**

**First page**

**Last page**

#### Abstract

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.

#### Keywords

#### Full Text:

PDF#### References

bibitem{Abedi}E. Abedi, R. Bahrami, M. M. Tirpathi, {it Ricci and Scalar curvatures of submanifolds of a conformal Sasakian space form}, Archivum Mathematicum (BRNO) Tomus {bf{52}} (2016), 113-130.

bibitem{Bishop} R. L. Bishop and B. O'Neil, {it Manifolds of negative curvature}, Trans. Amer. Math. Soc. {bf{145}} (1969), 1-9.

bibitem{Blair} D. E. Blair, {it Contact manifolds in Riemannian geometry}, Lecture Notes in Mathematics, {bf{509}}. Springer-Verlag, New York, (1976).

bibitem{Chen1} B. Y. Chen, {it Geometry of warped product CR-submanifold in Kaehler manifolds}, Monatsh. Math. {bf{133}} (3) (2001), 177-195.

bibitem{Chen2} B, Chen, {it On isometric minimal immersion from warped product submanifolds into real space forms}, Proc. Edinburgh Math. Soc. (2002), 579-587.

bibitem{Chen5} B.-Y. Chen, O. J. Gray, {it Pointwise slant submanifolds in almost Hermitian manifolds}, Turk. J. Math. {bf{79}} (2012), 630-640.

bibitem{Chen6} B.-Y. Chen, {it Pseudo-Riemannian geometry, $delta$-invariants and applications}, World Scientific, Hackensack, NJ, (2011).

bibitem{Chen7} B.-Y. Chen, S. Uddin, {it Warped product pointwise bi-slant submanifolds of Kaehler manifolds}, Publ. Math. Debrecen (1-2) {bf{92}} (2018), 183-199.

bibitem{Meraj}M. A. Khan, K.Khan, {it Bi-warped product submanifolds of complex space forms}, International Journal of Geometric methods in Modern Physics, {bf{16}}, 05, (2019).

bibitem{Murathan} C. Murathan, K. Arslan, R. Ezentas and I. Mihai, {it warped product submanifolds in Kenmotsu space forms}, Taiwanese J. Math. {bf{1}} (2006), 1431-1441.

bibitem{Nash} J. F. Nash, {it The imbedding problem for Riemannian manifold}, Ann. Math. {bf{63}} (1956), 20-63.

bibitem{Olteanu1} A. Olteanu, {it A general inequality of doubly warped product submanifolds}, Math J. Okayama Univ, {bf{52}} (2010), 133-142.

bibitem{Olteanu2} A. Olteanu, {it Doubly warped product in S-space forms}, Roman J. Math and Comp. Science {bf(4)} (2014), 111-124.

bibitem{Qua} Q. Qua, Y. Wang, {it Multiply warped products with a quarter-symmetric connection}, J. Math. Anal. Appl., {bf{431}} (2015), 955-987.

bibitem{Aliya}A. N. Siddiqui, M. H. Shahid, J. W. Lee, {it Geometric inequalities for warped product bi-slant submanifolds with a warping function}, J. Inequal Appl {bf265} (2018).

bibitem{Sular} S. Sular, {it Doubly warped product submanifolds a Riemannian manifold of quasi-constant curvature}, Annals of the Alexandru Ioan Cuza Univ. Maths, {bf{61}}, 1 (2015), 235-244.

bibitem{Unal} B. Unal, {it Doubly warped products}, Differ. Geom. App. {bf{15}} (3) (2001), 253-263.

bibitem{Wang}Y. Wang, {it Chen Inequalities for submanifold of complex space forms and Sasakian space forms with quarter-symmetric connections}, Int. J. Geom. Methods Mod. Phy. {bf{16}} (2019), 1950118.

bibitem{Yoon2} D. W. Yoon, K. S. Cho and S. G. Han, {it Some inequalities of warped products of locally conformal almost cosympelctic manifolds}, Note. di. Matematics. {bf{23}} (2004),51-60.

bibitem{Yoon3} D. W. Yoon, {it Inequality for Ricci curvature of certain submanifolds in locally conformal almost cosymplectic manifolds}, International Journal of Mathematics and Mathematical Sciences, {bf{10}} (2005), 1621-1632.

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)