جامعة أم القرى

جامعة أم القرى

مستخلص رسالة الماجستير إنجليزي


- 2016/08/11

ABSTRACT

The Title of thesis " On The Warped Product Manifolds" 

The objective of the present study is to investigate the existence of certain

warped product submanifolds in the setting of Kaehler, locally conformal Kaehler

(l.c.K.) and nearly Kaehler manifolds.

The notion of warped product manifolds as submanifolds of Kaehler manifolds

was introduced by B. Y. Chen. He showed that the warped product

CR-submanifolds are trivial in Kaehler manifolds. However,

the CR-warped product submanifolds (obtained by reversing the two factors)

are non-trivial. Various examples of these warped product submanifolds are

 provided and some fundamental geometric properties of these submanifolds are

 obtained in this thesis. His findings have been presented in Chapter 3.

For the sake of completeness and as prelude to the study of CR-warped product

and generic warped product submanifolds, an account of the important geometric

features of these submanifolds in Kaehler, l.c.K and nearly Kaehler manifolds

given in Chapter 2.

In view of the physical applications of the warped product submanifolds,

B.Sahin explored a more general class of warped product submanifolds, namely

semi-slant submanifolds as warped product submanifolds of a Kaehler manifold.

 He proved that the only non-trivial semi-slant warped product submanifolds of a

 Kaehler manifolds are CR-warped product submanifolds.

V. A. Khan et. al.  further extended the study by investigating the generic warped

 product submanifold of l.c.K. and nearly Kaehler manifolds. Many interesting the

 geometric properties of these submanifolds are obtained in the thesis. Some

 relevant result of these studies are presented in Chapter 4 and 5.

Motivated by the study, the Author has studied doubly warped product

 submanifolds of nearly Kaehler manifolds and proved that there does not exist

 proper doubly warped product submanifolds of nearly Kaehler manifolds with are

 factors a holomorphic submanifold. This study helped to derive many important

 geometric properties of generic warped product submanifolds of a nearly

Kaehler manifold.

 

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