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Author: Sadahiro Maeda
Publisher: World Scientific
ISBN: 9814566292
Category : Mathematics
Languages : en
Pages : 308
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Book Description
This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory. It also contains new results or brief surveys in these areas. This volume provides fundamental knowledge to readers (such as differential geometers) who are interested in the theory of real hypersurfaces in a non-flat complex space form. Contents:Homogeneous Submanifolds and Homogeneous Curves in Space Forms (S Maeda)Injectivity Property of Regular Curves and a Sphere Theorem (O Kobayashi)A Family of Complete Minimal Surfaces of Finite Total Curvature with Two Ends (S Fujimori and T Shoda)Minimal Surfaces in the Anti-De Sitter Spacetime (T Ichiyama and S Udagawa)Extrinsic Circular Trajectories on Geodesic Spheres in a Complex Projective Space (T Adachi)Geometry of Certain Lagrangian Submanifolds in Hermitian Symmetric Spaces (Y Ohnita)Some Real Hypersurfaces of Complex Projective Space (T Hamada)Contact Metric Hypersurfaces in Complex Space Forms (J T Cho and J Inoguchi)Non-Homogeneous η-Einstein Real Hypersurfaces in a 2-Dimensional Nonflat Complex Space Form (K Okumura)Sectional Curvatures of Ruled Real Hypersurfaces in a Nonflat Complex Space Form (H Tanabe and S Maeda)Totally Geodesic Köhler Immersions into a Complex Space Form, and a Non-Existence Theorem for Hessian Metrics of Positive Constant Hessian Sectional Curvature (T Noda and N Boumuki)Archimedean Theorems and W-Curves (D-S Kim and Y H Kim)On the Construction of Cohomogeneity One Special Lagrangian Submanifolds in the Cotangent Bundle of the Sphere (K Hashimoto)Self-Shrinkers of the Mean Curvature Flow (Q-M Cheng and Y Peng)Spectrum of Poly-Laplacian and Fractional Laplacian (L Zeng)Flat Centroaffine Surfaces with Non-Semisimple Tchebychev Operator (A Fujioka)The Total Absolute Curvature of Open Curves in EN (K Enomoto and J Itoh)Antipodal Sets of Compact Symmetric Spaces and the Intersection of Totally Geodesic Submanifolds (M S Tanaka)A Note on Symmetric Triad and Hermann Action (O Ikawa)Some Topics of Homogeneous Submanifolds in Complex Hyperbolic Spaces (T Hashinaga, A Kubo and H Tamaru)Austere Hypersurfaces in 5-Sphere and Real Hypersurfaces in Complex Projective Plane (J T Cho and M Kimura)On the Minimality of Normal Bundles in the Tangent Bundles Over the Complex Space Forms (T Kajigaya)Over-Determined Systems on Surfaces (N Ando) Readership: Researchers in differential geometry. Keywords:Minimal Surfaces;Morse Index;Real Hypersurfaces;Non-flat Complex Space Forms;Hopf Hypersurfaces;Symmetric Spaces;Homogeneous CurvesKey Features:Interesting papers on the theory of real hypersurfaces and the theory of minimal surfacesFeatures prominent contributors such as Y Ohnita, Q-M Cheng and O Kobayashi
Author: Sadahiro Maeda
Publisher: World Scientific
ISBN: 9814566292
Category : Mathematics
Languages : en
Pages : 308
Get Book
Book Description
This volume is a compilation of papers presented at the conference on differential geometry, in particular, minimal surfaces, real hypersurfaces of a non-flat complex space form, submanifolds of symmetric spaces and curve theory. It also contains new results or brief surveys in these areas. This volume provides fundamental knowledge to readers (such as differential geometers) who are interested in the theory of real hypersurfaces in a non-flat complex space form. Contents:Homogeneous Submanifolds and Homogeneous Curves in Space Forms (S Maeda)Injectivity Property of Regular Curves and a Sphere Theorem (O Kobayashi)A Family of Complete Minimal Surfaces of Finite Total Curvature with Two Ends (S Fujimori and T Shoda)Minimal Surfaces in the Anti-De Sitter Spacetime (T Ichiyama and S Udagawa)Extrinsic Circular Trajectories on Geodesic Spheres in a Complex Projective Space (T Adachi)Geometry of Certain Lagrangian Submanifolds in Hermitian Symmetric Spaces (Y Ohnita)Some Real Hypersurfaces of Complex Projective Space (T Hamada)Contact Metric Hypersurfaces in Complex Space Forms (J T Cho and J Inoguchi)Non-Homogeneous η-Einstein Real Hypersurfaces in a 2-Dimensional Nonflat Complex Space Form (K Okumura)Sectional Curvatures of Ruled Real Hypersurfaces in a Nonflat Complex Space Form (H Tanabe and S Maeda)Totally Geodesic Köhler Immersions into a Complex Space Form, and a Non-Existence Theorem for Hessian Metrics of Positive Constant Hessian Sectional Curvature (T Noda and N Boumuki)Archimedean Theorems and W-Curves (D-S Kim and Y H Kim)On the Construction of Cohomogeneity One Special Lagrangian Submanifolds in the Cotangent Bundle of the Sphere (K Hashimoto)Self-Shrinkers of the Mean Curvature Flow (Q-M Cheng and Y Peng)Spectrum of Poly-Laplacian and Fractional Laplacian (L Zeng)Flat Centroaffine Surfaces with Non-Semisimple Tchebychev Operator (A Fujioka)The Total Absolute Curvature of Open Curves in EN (K Enomoto and J Itoh)Antipodal Sets of Compact Symmetric Spaces and the Intersection of Totally Geodesic Submanifolds (M S Tanaka)A Note on Symmetric Triad and Hermann Action (O Ikawa)Some Topics of Homogeneous Submanifolds in Complex Hyperbolic Spaces (T Hashinaga, A Kubo and H Tamaru)Austere Hypersurfaces in 5-Sphere and Real Hypersurfaces in Complex Projective Plane (J T Cho and M Kimura)On the Minimality of Normal Bundles in the Tangent Bundles Over the Complex Space Forms (T Kajigaya)Over-Determined Systems on Surfaces (N Ando) Readership: Researchers in differential geometry. Keywords:Minimal Surfaces;Morse Index;Real Hypersurfaces;Non-flat Complex Space Forms;Hopf Hypersurfaces;Symmetric Spaces;Homogeneous CurvesKey Features:Interesting papers on the theory of real hypersurfaces and the theory of minimal surfacesFeatures prominent contributors such as Y Ohnita, Q-M Cheng and O Kobayashi
Author: Y. L. Xin
Publisher: World Scientific
ISBN: 9812386874
Category : Mathematics
Languages : en
Pages : 271
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Book Description
The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and author's own contributions to Bernstein type theorems for higher codimensions. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
Author: Bang-Yen Chen
Publisher: Courier Dover Publications
ISBN: 0486832783
Category : Mathematics
Languages : en
Pages : 193
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Book Description
The first two chapters of this frequently cited reference provide background material in Riemannian geometry and the theory of submanifolds. Subsequent chapters explore minimal submanifolds, submanifolds with parallel mean curvature vector, conformally flat manifolds, and umbilical manifolds. The final chapter discusses geometric inequalities of submanifolds, results in Morse theory and their applications, and total mean curvature of a submanifold. Suitable for graduate students and mathematicians in the area of classical and modern differential geometries, the treatment is largely self-contained. Problems sets conclude each chapter, and an extensive bibliography provides background for students wishing to conduct further research in this area. This new edition includes the author's corrections.
Author: M.A. Akivis
Publisher: Elsevier
ISBN: 0080887163
Category : Mathematics
Languages : en
Pages : 375
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Book Description
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations. Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.
Author: Luc Vrancken
Publisher: Lulu.com
ISBN: 1847990169
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).
Author: Xin Yuanlong
Publisher: World Scientific
ISBN: 9813236078
Category : Mathematics
Languages : en
Pages : 396
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Book Description
In the theory of minimal submanifolds, Bernstein's problem and Plateau's problem are central topics. This important book presents the Douglas-Rado solution to Plateau's problem, but the main emphasis is on Bernstein's problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and the author's own contributions to Bernstein type theorems for higher codimension. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds. This new edition contains the author's recent work on the Lawson-Osserman's problem for higher codimension, and on Chern's problem for minimal hypersurfaces in the sphere. Both Chern's problem and Lawson-Osserman's problem are important problems in minimal surface theory which are still unsolved. In addition, some new techniques were developed to address those problems in detail, which are of interest in the field of geometric analysis.
Author: Peter W. Michor
Publisher: American Mathematical Soc.
ISBN: 0821820036
Category : Geometry, Differential
Languages : en
Pages : 510
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Book Description
"This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.
Author: Bang-Yen Chen
Publisher: Springer Nature
ISBN: 981999750X
Category :
Languages : en
Pages : 230
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Book Description
Author: Stefan Haesen
Publisher: Springer
ISBN: 9462392404
Category : Mathematics
Languages : en
Pages : 284
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Book Description
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Author: Gu Chaohao
Publisher: World Scientific
ISBN: 9814487309
Category : Mathematics
Languages : en
Pages : 292
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Book Description
The International Conference on Modern Mathematics and the International Symposium on Differential Geometry, in honor of Professor Su Buchin on the centenary of his birth, were held in September 2001 at Fudan University, Shanghai, China. Around 100 mathematicians from China, France, Japan, Singapore and the United States participated. The proceedings cover a broad spectrum of advanced topics in mathematics, especially in differential geometry, such as some problems of common interest in harmonic maps, submanifolds, the Yang-Mills field and the geometric theory of solitons. Contents:Asymptotic Behavior of Yang–Mills Flow in Higher Dimensions (Y M Chen et al.)Complete Submanifolds in Euclidean Spaces with Constant Scalar Curvature (Q M Cheng)On Mathematical Ship Lofting (G C Dong et al.)On the Nirenberg Problem (M Ji)Almost Complex Manifolds and a Differential Geometric Criterion for Hyperbolicity (S Kobayashi)Harmonic Maps Between Carnot Spaces (S Nishikawa)A Survey of Complete Manifolds with Bounded Radial Curvature Function (K Shiohama)On the Hensel Lift of a Polynomial (Z X Wan)A Note on Locally Real Hyperbolic Space with Finite Volume (Y H Yang)and other papers Readership: Researchers and graduate students in mathematics. Keywords:Differential Geometry;Harmonic Map;Submanifold;Yang-Mills Field;Geometric Theory of Solitons;Cohomology
