arXiv subjects

Falleh R. Al-Solamy

Publications and source records attributed to Falleh R. Al-Solamy.

6 recordsLinked to original sources

arXiv2020

Geometry of contact skew CR-warped product submanifolds of Sasakian manifolds

In this paper, we study warped products of contact skew-CR submanifolds, called contact skew CR-warped products. We establish an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. The equality case in the statement of the inequality is investigated and some applications of derived inequality are given. Furthermore, we provide a non-trivial example of such submanifolds.

math.DG↗

arXiv2020

On CR-statistical submanifolds of holomorphic statistical manifolds

In the present paper, we investigate some properties of the distributions involved in the definition of a CR-statistical submanifold. The characterization of a CR-product in holomorphic statistical manifolds is given. By using an optimization technique, we establish a relationship between the Ricci curvature and the squared norm of the mean curvature of any submanifold in the same ambient space. The equality case is also discussed here. This paper finishes with some related examples.

math.DG↗

arXiv2017

A general inequality for contact CR-warped product submanifolds in cosymplectic space forms

B.-Y. Chen initiated the study of warped product submanifolds in his fundamental seminal papers \cite{C1,C2,C2.1}. In this paper, we study contact CR-warped product submanifolds of cosymplectic space forms and prove an optimal inequality by using Gauss and Codazzi equations. In addition, we obtain two geometric inequalities for contact CR-warped product submanifolds with a compact invariant factor.

math.DG↗

arXiv2014

An optimal inequality on warped product semi-slant submanifolds of nearly Kaehler manifolds

Non-existence of warped product semi-slant submanifolds of Kaehler manifolds was proved in [17], it is interesting to find their existence. In this paper, we prove the existence of warped product semi-slant submanifolds of nearly Kaehler manifolds by a characterization. To this end we obtain an inequality for the squared norm of second fundamental form in terms of the warping function and the slant angle. The equality case is also discussed.

math.DG↗

arXiv2013

Two optimal inequalities for anti-holomorphic submanifolds and their applications

The CR $δ$-invariant for CR-submanifolds was introduced in a recent article [B. Y. Chen, An optimal inequality for CR-warped products in complex space forms involving CR $δ$-invariant, Internat. J. Math. 23} (2012), no. 3, 1250045 (17 pages)]. In this paper, we prove two new optimal inequalities for anti-holomorphic submanifolds in complex space forms involving the CR $δ$-invariant. Moreover, we obtain some classification results for certain anti-holomorphic submanifolds in complex space forms which satisfy the equality case of either inequality.

math.DG↗

arXiv2000

A generalised Hopf algebra for solitons

This paper considers a generalisation of the idea of a Hopf algebra in which a commutative ring replaces the field in the unit and counit. It is motivated by an example from the inverse scattering formalism for solitons. We begin with the corresponding idea for groups, where the concept of the identity is altered.

math.QA↗