NATIONAL BIBLIOGRAPHY NUMBER
Number
۵۶۵۷پ
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
per
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
بازیابی یک خمینه با تانسور متری داده شده
First Statement of Responsibility
/یاسر افتخاری
.PUBLICATION, DISTRIBUTION, ETC
Name of Publisher, Distributor, etc.
دانشگاه تبریز: دانشکده علوم ریاضی، گروه ریاضی محض
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
۱۳۶ص
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
چاپی
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
دکتر مگردیچ تومانیان
CONTENTS NOTE
Text of Note
فاقد چکیده و کلیدواژه فارسی و فایل pdf
DISSERTATION (THESIS) NOTE
Dissertation or thesis details and type of degree
کارشناسی ارشد
Discipline of degree
ریاضی محض(هندسه)
Date of degree
۱۳۸۵/۰۹/۲۵
Body granting the degree
دانشگاه تبریز: دانشکده علوم ریاضی، گروه ریاضی محض
SUMMARY OR ABSTRACT
Text of Note
In this thesis, we first provide a proof of the fundamental theorem of surfaces by showing how it can be established as a simple corollary of another theorem of differential geometry which asserts that: if the Riemannian-Christoffel tensor associated with a field of positive definite symmetric matrices of order three vanishes in a connected open subset of , then this field is the metric tensor field of an open set that can be isometrically imbedded in and this open set is unique up to isometries in . Secondly, we will establish that a surface varies continuously as a function of its two fundamental forms, for certain natural topologies. A classical theorem in geometry asserts that if a -metric tensor satisfies the Riemann compatibility conditions, then it is induced by an immersion. In here, it is established that this theorem holds true for -metric tensor satisfying the Riemann compatibility conditions in a distributional sense. Finally, it is proved that the fundamental theorem of surfaces holds true under the weaker regularity assumptions that two fundamental forms of it are of class and respectively and the Gauss and Codazzi-Mainardi equations being understood in a distributional sense
TOPICAL NAME USED AS SUBJECT
Riemannian space
Isometric immersions
Distributions
Riemann Compatibility conditions
PERSONAL NAME - PRIMARY RESPONSIBILITY
افتخاری، یاسر
PERSONAL NAME - SECONDARY RESPONSIBILITY
تومانیان، مگردیچ، استادراهنما
پوررضا، ابراهیم، استادمشاور
ELECTRONIC LOCATION AND ACCESS
Public note
سیاه و سفید
نمایه‌سازی قبلی
