Abstract
We study warped product of the typeNθ×fNTandNθ×fN⊥, whereNθ,NT, andN⊥are proper slant, invariant, and anti-invariant submanifolds, respectively, and we prove some basic results and finally obtain some inequalities for squared norm of second fundamental form.
Highlights
Bishop and O’Neil 1 introduced the notion of warped product manifolds that occur naturally; for example, surface of revolution is a warped product manifold
A submanifold M of a Riemannian product manifold is called hemi-slant submanifold if it is endowed with two orthogonal complementary distributions D⊥ and Dθ such that D⊥ is totally real and Dθ is slant distribution with slant angle θ / π/2
For a warped product manifold N1×f N2, we denote by D1 and D2 the distributions defined by the vectors tangent to the leaves and fibers, respectively
Summary
Bishop and O’Neil 1 introduced the notion of warped product manifolds that occur naturally; for example, surface of revolution is a warped product manifold. In 4 Atceken studied semi-slant warped product of Riemannian product manifolds. They proved that there exists no warped product if spheric submanifold of warped product submanifold is proper slant submanifold. On the other hand they proved the existence of warped product of the type Nθ×f NT and Nθ×f N⊥ via some examples. In this continuation we have studied the warped product submanifolds in which proper slant submanifolds are totally geodesic; that is, we study the warped product of the types Nθ × NT and Nθ × N⊥ and called them semi-slant warped product and hemi-slant warped product submanifolds, respectively
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