Document Details

Document Type : Thesis 
Document Title :
on warped product manifolds
على متعددات الضرب المفتول
 
Subject : Faculty of Sciences 
Document Language : Arabic 
Abstract : 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 [19]. 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 [19]. His _ndings 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 [49] explored a more general class of warped product submanifolds, namely semi-slant submanifolds as warped product submanifolds of a Kaehler manifold. He proved in [49] that the only non-trivial semi-slant warped product submanifolds of a Kaehler manifolds are CR-warped product submanifolds. V. A. Khan et. al. [33] and [40] 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 [33], [40] and [49]. 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. 
Supervisor : Dr .Waqar Ahmed Gulzar 
Thesis Type : Master Thesis 
Publishing Year : 1431 AH
2010 AD 
Co-Supervisor : dr.Mohammed Mosa Al-Shomrani 
Added Date : Saturday, May 8, 2010 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
أماني علي الكثيريAL-KATHIRY, AMANI ALIResearcherMaster 

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