Siraj Uddin

An inequality for contact CR-warped product submanifolds of nearly cosymplectic manifolds

Recently, Chen (Monatshefte Math. 133:177-195, 2001) established general sharp inequalities for CR-warped products in a Kaehler manifold. Afterward, Mihai obtained (Geom. Dedic. 109:165-173, 2004) the same inequalities for contact CR-warped product submanifolds of Sasakian space forms and derived some applications. In this paper, we obtain an inequality for the length of the second fundamental form of the warped product submanifold of a nearly cosymplectic manifold in terms of the warping function. The equality case is also discussed.MSC:53C40, 53C42, 53B25.

Semi-invariant warped product submanifolds of cosymplectic manifolds

In this article, we obtain the necessary and sufficient conditions that the semi-invariant submanifold to be a locally warped product submanifold of invariant and anti-invariant submanifolds of a cosymplectic manifold in terms of canonical structures T and F. The inequality and equality cases are also discussed for the squared norm of the second fundamental form in terms of the warping function.2000 AMS Mathematics Subject Classification: 53C25; 53C40; 53C42; 53D15.

Warped Product Semi-Invariant Submanifolds of Nearly Cosymplectic Manifolds

We study warped product semi-invariant submanifolds of nearly cosymplectic manifolds. We prove that the warped product of the type 𝑀⟂×𝑓𝑀𝑇 is a usual Riemannian product of 𝑀⟂ and 𝑀𝑇, where 𝑀⟂ and 𝑀𝑇 are anti-invariant and invariant submanifolds of a nearly cosymplectic manifold 𝑀, respectively. Thus we consider the warped product of the type 𝑀𝑇×𝑓𝑀⟂ and obtain a characterization for such type of warped product.

A note on warped product submanifolds of cosymplectic manifolds

In this paper, we study warped product anti-slant submanifolds of cosymplectic manifolds. It is shown that the cosymplectic manifold do not admit non trivial warped product submanifolds in the form N⊥ ×fNθ and then we obtain some results for the existence of warped products of the type Nθ ×fN⊥, where N⊥ and Nθ are anti-invariant and proper slant submanifolds of a cosymplectic manifold M¯ , respectively.

Geometry of warped product semi-slant submanifolds of Kenmotsu manifolds

In this paper, we study semi-slant submanifolds and their warped products in Kenmotsu manifolds. The existence of such warped products in Kenmotsu manifolds is shown by an example and a characterization. A sharp relation is obtained as a lower bound of the squared norm of second fundamental form in terms of the warping function and the slant angle. The equality case is also considered in this paper. Finally, we provide some applications of our derived results.

Totally Umbilical Hemi-Slant Submanifolds of Kaehler Manifolds

We study totally umbilical hemi-slant submanifolds of a Kaehler manifold via curvature tensor. We prove some classification theorems for totally umbilical hemi-slant submanifolds of a Kaehler manifold and give an example.

Geometry of warped product pseudo-slant submanifolds of Kenmotsu manifolds

Abstract In this paper, we study pseudo-slant submanifolds and their warped products in Kenmotsu manifolds. We obtain the necessary conditions that a pseudoslant submanifold is locally a warped product and establish an inequality for the squared norm of the second fundamental form in terms of the warping function. The equality case is also considered.

Warped Product Pseudo-Slant Submanifolds of a Nearly Cosymplectic Manifold

We study warped product pseudo-slant submanifolds of a nearly cosymplectic manifold. We obtain some characterization results on the existence or nonexistence of warped product pseudo-slant submanifolds of a nearly cosymplectic manifold in terms of the canonical structures 𝑃 and 𝐹.

Some Results on Warped Product Submanifolds of a Sasakian Manifold

We study warped product Pseudo-slant submanifolds of Sasakian manifolds. We prove a theorem for the existence of warped product submanifolds of a Sasakian manifold in terms of the canonical structure 𝐹.

Submanifolds of generalized

In this paper, we have studied submanifolds especially, totally umbilical submanifolds of generalized