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J Inequal Appl. 2018;2018(1):265. doi: 10.1186/s13660-018-1843-3. Epub 2018 Sep 27.

Geometric inequalities for warped product bi-slant submanifolds with a warping function.

Author information

1Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi, India.
2Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, South Korea.


In this paper, we prove that the squared norm of the second fundamental form for bi-slant submanifolds with any codimension of nearly trans-Sasakian manifolds is bounded below by the gradient of a warping function and also find the conditions on which the equality holds. Some related examples are also provided.


Bi-slant submanifolds; Nearly trans-Sasakian manifolds; Warped product bi-slant submanifolds

Conflict of interest statement

The authors declare that they have no competing interests.

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