The classification problems of finite type and biharmonic submanifolds 有限型部分多様体および二重調和部分多様体の分類問題
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Bibliographic Information
- Title
-
The classification problems of finite type and biharmonic submanifolds
- Other Title
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有限型部分多様体および二重調和部分多様体の分類問題
- Author
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石川, 晋
- Author(Another name)
-
イシカワ, ススム
- University
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九州大学
- Types of degree
-
理学博士
- Grant ID
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乙第5242号
- Degree year
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1992-09-25
Note and Description
博士論文
Chapter I.Introduction Chapter II.General Notation Chapter III.Finite Type Curves Chapter IV.The Finite Type Surfaces of Revolution in E^3 Chapter V.Topics Related to Finite Type Submanifolds Theory Chapter VI.Biharmonic Submanifolds Chapter VII.Biharmonic Surfaces in[数式]
数学
Table of Contents
- Contents / p1 (0004.jp2)
- Preface / p3 (0006.jp2)
- Chapter I.Introduction / p5 (0008.jp2)
- §1.1.Chen's Conjecture Concerning Biharmonic Submanifolds / p5 (0008.jp2)
- §1.2.Chen's Conjecture Concerning Finite Type Surfaces in E³ / p7 (0010.jp2)
- §1.3.Finite type Closed Curves on Hyperbolic spaces / p9 (0012.jp2)
- Chapter II.General Notation / p11 (0014.jp2)
- §2.1.Pseudo-Riemannian Manifolds / p11 (0014.jp2)
- §2.2.Finite Type Submanifolds in Euclidean and Pseudo-Euclidean Spaces / p16 (0019.jp2)
- Chapter III.Finite Type Curves / p20 (0023.jp2)
- §3.1.Results on Finite Type Closed Curves in[数式],[数式]and[数式] / p20 (0023.jp2)
- §3.2.The Classification Problem of Finite Type Closed Curves on[数式](-c²) / p23 (0026.jp2)
- §3.3.Proofs of Theorems 3.5,3.6,3.7,3.8 and 3.9 / p24 (0027.jp2)
- Chapter IV.The Finite Type Surfaces of Revolution in E³ / p33 (0036.jp2)
- §4.1.The Classification Problem of Finite Type Surfaces in E³ / p33 (0036.jp2)
- §4.2.The Classification of Surfaces of Revolution I / p34 (0037.jp2)
- §4.3.The Classification of Surfaces of Revolution II / p42 (0045.jp2)
- Chapter V.Topics Related to Finite Type Submanifolds Theory / p47 (0050.jp2)
- §5.1.Examples of Finite Type Surfaces / p47 (0050.jp2)
- §5.2.Related Topics / p50 (0053.jp2)
- Chapter VI.Biharmonic Submanifolds / p54 (0057.jp2)
- §6.1.General Results on Biharmonic Submanifolds / p54 (0057.jp2)
- §6.2.The classification Problem of all Biharmonic Curves in[数式] / p56 (0059.jp2)
- §6.3.The Non-Existence Theorems of Non-Harmonic Biharmonic Surfaces in[数式] / p59 (0062.jp2)
- Chapter VII.Biharmonic Surfaces in[数式] / p62 (0065.jp2)
- §7.1.Fundamental Formulae on Biharmonic Surfaces in[数式] / p62 (0065.jp2)
- §7.2.Biharmonic Surfaces with Nonzero Constant Mean Curvature vector Fields in[数式] / p63 (0066.jp2)
- §7.3.Biharmonic Surfaces with Light-like Mean Curvature Vector Fields in[数式] / p71 (0074.jp2)
- §7.4.Biharmonic W-Surfaces in[数式] / p77 (0080.jp2)
- References / p88 (0091.jp2)