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Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry

2020-04-04 Mathematics
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Release : 2020-04-04
Genre : Mathematics
Kind : eBook
Book Rating : 392/5 ( reviews)

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Book Synopsis Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry by : Ye-lin Ou

Download or read book Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry written by Ye-lin Ou. This book was released on 2020-04-04. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results.Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces.Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics.Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained.This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field.

Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods

2018-12-06 Mathematics
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Release : 2018-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 418/5 ( reviews)

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Book Synopsis Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods by : Hajime Urakawa

Download or read book Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods written by Hajime Urakawa. This book was released on 2018-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 'The present volume, written in a clear and precise style, ends with a rich bibliography of 167 items, including some classical books and papers. In the reviewer’s opinion, this excellent monograph will be a basic reference for graduate students and researchers working in the field of differential geometry of variational methods.'zbMATHThe author describes harmonic maps which are critical points of the energy functional, and biharmonic maps which are critical points of the bienergy functional. Also given are fundamental materials of the variational methods in differential geometry, and also fundamental materials of differential geometry.

Differential Geometry - Proceedings Of The Viii International Colloquium

2009-04-27 Mathematics
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Release : 2009-04-27
Genre : Mathematics
Kind : eBook
Book Rating : 460/5 ( reviews)

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Book Synopsis Differential Geometry - Proceedings Of The Viii International Colloquium by : Jesus A Alvarez Lopez

Download or read book Differential Geometry - Proceedings Of The Viii International Colloquium written by Jesus A Alvarez Lopez. This book was released on 2009-04-27. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's and Thurston-Bennequin's inequalities, a discussion about Fatou-Julia decompositions for foliations and a description of singular Riemannian foliations on spaces without conjugate points.Papers on submanifold theory focus on the existence of graphs with prescribed mean curvature and mean curvature flow for spacelike graphs, isometric and conformal deformations and detailed surveys on totally geodesic submanifolds in symmetric spaces, cohomogeneity one actions on hyperbolic spaces and rigidity of geodesic spheres in space forms. Geometric realizability of curvature tensors and curvature operators are also treated in this volume with special attention to the affine and the pseudo-Riemannian settings. Also, some contributions on biharmonic maps and submanifolds enrich the scope of this volume in providing an overview of different topics of current interest in differential geometry.

Symposium on the Differential Geometry of Submanifolds

2008-06-30 Mathematics
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Release : 2008-06-30
Genre : Mathematics
Kind : eBook
Book Rating : 169/5 ( reviews)

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Book Synopsis Symposium on the Differential Geometry of Submanifolds by : Luc Vrancken

Download or read book Symposium on the Differential Geometry of Submanifolds written by Luc Vrancken. This book was released on 2008-06-30. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Harmonic Maps and Differential Geometry

2011 Mathematics
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Release : 2011
Genre : Mathematics
Kind : eBook
Book Rating : 875/5 ( reviews)

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Book Synopsis Harmonic Maps and Differential Geometry by : Eric Loubeau

Download or read book Harmonic Maps and Differential Geometry written by Eric Loubeau. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7-10, 2009, to celebrate John C. Wood's 60th birthday. These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kahler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces.

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