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Document Details
Document Type
:
Thesis
Document Title
:
Geometry of tangent bundles of some almost hermition manifolds
هندسة الحزم المماسية لبعض عديدات الطيات الهرمتية تقريبًا
Subject
:
Mathematics
Document Language
:
Arabic
Abstract
:
Geometry of tangent bundle T M of a Riemannian manifold (M, g) with the metric fj defined by Sasaki [25] has been extensively studied since the 60s. Ex- plicit expressions for the Lie bracket of the tangent bundle T M was given by Dombrowski [10]. The Levi-Civita connection of the Sasaki metric on T M and its Riemannian curvature tensor were calculated by Kowalski [14] . Another met- ric nicely fitted to the tangent bundle is the so-called Cheeger-Gromoll metric [8] . It was expressed more explicitly by Mussu and Tricerri [20] . Sekizawa [26] calcu- lated the Levi-Civita connection and the curvature tensor of the tangent bundle equipped with Cheeger-Gromoll metric. The geometry of totally geodesic sub- manifold of the tangent bundle was studied by Abbassi and Yambolsky [3] .Very recently, Marian [19] has introduced a metric called the general metric which generalizes the above mentioned metrics. The aim of this thesis is to give a detailed presentation of some of the most important results in the field. We have also studied tangent sphere bundle as a hypersurface of the tangent bundle of a Riemannian manifold and discussed some curvature properties of the tangent sphere bundle equipped with the induced Sasaki metric and Cheeger-Gromoll metric. Moreover, in the last chapter, we have obtained some new results on the tangent sphere bundle with the general metric
Supervisor
:
Dr. Mohamed Hassan Shahd
Thesis Type
:
Master Thesis
Publishing Year
:
1427 AH
2006 AD
Co-Supervisor
:
Dr. Faleh RajaaAllah Al-Sulami
Added Date
:
Wednesday, June 11, 2008
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
غاده سمير مطر
Matar, Ghada Sameer
Researcher
Master
gmatar@kau.edu.sa
Files
File Name
Type
Description
23708.pdf
pdf
المستخلص
23709.pdf
pdf
Abstract
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