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

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

Abstract

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.

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