Meraj Ali Khan

SLANT AND SEMI-SLANT SUBMANIFOLDS OF A KENMOTSU MANIFOLD

In the present note we have obtained some basic results pertaining to the geometry of slant and semi-slant submanifolds of a Kenmotsu manifold.

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.

Semi-Slant Warped Product Submanifolds of a Kenmotsu Manifold

We study semi-slant warped product submanifolds of a Kenmotsu manifold. We obtain a characterization for warped product submanifolds in terms of warping function and shape operator and finally proved an inequality for squared norm of second fundamental form.

Semi-invariant warped product submanifolds of almost contact manifolds

In this article, we have obtained necessary and sufficient conditions in terms of canonical structure F on a semi-invariant submanifold of an almost contact manifold under which the submanifold reduced to semi-invariant warped product submanifold. Moreover, we have proved an inequality for squared norm of second fundamental form and finally, an estimate for the second fundamental form of a semi-invariant warped product submanifold in a generalized Sasakian space form is obtained, which extend the results of Chen, Al-Luhaibi et al., and Hesigawa and Mihai in a more general setting.2000 Mathematics Subject Classification: 53C25; 53C40; 53C42; 53D15.

Warped Product Submanifolds of Riemannian Product Manifolds

We study warped product of the type and , where , , and 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.

Hemi-Slant Warped Product Submanifolds of Nearly Kaehler Manifolds

Hemi-slant warped product submanifolds of nearly Kaehler manifolds are studied and some interesting results are obtained. Moreover, an inequality is established for squared norm of second fundamental form and equality case is also discussed. The results obtained are also true if ambient manifold is replaced by a Kaehler manifold. These results generalize several known results in the literature.

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.

Second-order duality for nondifferentiable minimax fractional programming problems with generalized convexity

In the present paper, we are concerned with second-order duality for nondifferentiable minimax fractional programming under the second-order generalized convexity type assumptions. The weak, strong and converse duality theorems are proved. Results obtained in this paper extend some previously known results on nondifferentiable minimax fractional programming in the literature.MSC:90C32, 49K35, 49N15.

Roughly geodesic B - r-preinvex functions on Cartan Hadamard manifolds

In this article, we introduce a new class of functions called roughly geodesic B????r???? preinvex on a Hadamard manifold and establish some properties of roughly geodesic B - r-preinvex functions on Hadamard manifolds. It is observed that a local minimum point for a scalar optimization problem is also a global minimum point under roughly geodesic B-r- preinvexity on Hadamard manifolds. The results presented in this paper extend and generalize the results appeared in the literature.