Warped product submanifolds of an S-manifold
Reem A. Al-Ghefari, Salha Altharwi · International Mathematical Forum · 2014
article distributed under the Creative Commons Attribution License, which permits unre-stricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper we prove that there does not exist warped product of the type Nθ ×λ NT and NT ×λ Nθ of an S-manifold, where Nθ and NT are the slant and invariant submanifold of an S-manifold.We observe that only warped product of the type NT ×λN ⊥ exist,with N⊥ as a anti-invariant submanifolds of an S-manifold.Some basic results are discussed for the warped product of the type NT ×λN ⊥ and finally,we prove an inequality for the squared norm of second fundamental form and equality case is also discussed.