Document Details

Document Type : Project 
Document Title :
Geometry of Warped Product
هندسة الضرب الالتفافي لعديدات الطيات الجزئية
 
Subject : Geometry of Warped Product 
Document Language : Arabic 
Abstract : Recently, many important physical applications of warped product manifolds have been discovered, giving impulse to the study of these spaces with differential geometric point of view. For instance, it has been realized that the warped product manifolds provide an excellent setting to model space-time near black holes or bodies with large gravitational fields ( [2 ], [3], [16] etc.). Consequently, many results are published showing the non-existence of warped product submanifolds in different settings. The object of the project is to investigate the existence of warped product manifolds in more general spaces and spaces of more physical utility than simply Kaehler or Sasakian manifolds. To investigate warped product submanifolds we wish to consider the settings of nearly Kaehler, Trans-Sasakian, and -manifolds etc. Moreover, the isometric immersion of a Riemannian manifold into an ambient manifold gives rise to the extrinsic invariants of the submanifold. Hence for the non trivial warped product submanifolds in the above mentioned spaces, there emerges a natural problem of finding the estimates of the squared norm of the second fundamental form and the mean curvature vector. Our aim is to workout these estimates which will predict the geometric behavior of the underlying warped product submanifolds. Further, as it is known that the warping function of a warped product manifold is a solution of some partial differential equation (cf. [8]) and most of the physical phenomenons are described by partial differential equation, we hope our study may find applications in Physics. 
Publishing Year : 1428 AH
2007 AD 
Sponsor Name : King Abdulalziz University 
Sponsorship Year : 1428 AH
2007 AD 
Added Date : Tuesday, July 6, 2010 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
وقار أعظم خانKhan, Viqar AzamInvestigatorDoctorate 

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 27350.docx docx 

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