1 edition of **Geometry of Harmonic Maps** found in the catalog.

- 239 Want to read
- 28 Currently reading

Published
**1996**
by Birkhäuser Boston in Boston, MA
.

Written in English

- Partial Differential equations,
- Mathematical physics,
- Materials,
- Global differential geometry,
- Mathematics,
- Distribution (Probability theory)

**Edition Notes**

Statement | by Yuanlong Xin |

Series | Progress in Nonlinear Differential Equations and Their Applications -- 23, Progress in nonlinear differential equations and their applications -- 23. |

Classifications | |
---|---|

LC Classifications | QA641-670 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (x, 242 pages). |

Number of Pages | 242 |

ID Numbers | |

Open Library | OL27041046M |

ISBN 10 | 1461286441, 1461240840 |

ISBN 10 | 9781461286448, 9781461240846 |

OCLC/WorldCa | 852791229 |

Siu, Y.-T., The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. Math. , 73– (). MathSciNet CrossRef zbMATH Google Scholar [S2]Cited by: 1. Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds, and K\{a}hlerian manifolds.

Book Description. This book is concerned with harmonic maps into homogeneous spaces and focuses upon maps of Riemann surfaces into flag manifolds, to bring results of 'twistor methods' for symmetric spaces into a unified framework by using the theory of compact Lie groups and complex differential geometry. A tale of two fractals. This book is devoted to a phenomenon of fractal sets, or simply fractals. Topics covered includes: Sierpinski gasket, Harmonic functions on Sierpinski gasket, Applications of generalized numerical systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets, Geometric and group-theoretic approach.

I) Introduction1 to CR geometry and subelliptic harmonic maps. II) Boundary values of Bergman-harmonic maps Sorin Dragomir2 Abstract. We give an elementary introduction to CR and pseu-dohermitian geometry, starting from H. Lewy’s legacy (cf. [20]) i.e. tangential Cauchy-Riemann equations on the boundary of the Siegel domain. Harmonic geometry is a site that is dedicated to the art of sacred geometry. Geometry plays apart in every aspect of life on earth and has been used by ancient civilisations to construct some of the architecture that we still visit today.

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Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the.

Geometry of Harmonic Maps by Yuanlong Xin,available at Book Depository with free delivery worldwide. Geometry of Harmonic Maps: Yuanlong Xin: We use cookies to give you the best possible experience. Harmonic Maps and Gauss Maps.- Generalized Gauss Maps.- Cone-like Harmonic Maps.- Generalized Maximum Principle.- Estimates of Image Diameter and its Applications.- Gauss Image of a Space-Like Hypersurface in Minkowski Space.- Gauss Image of a Space-Like Submanifold in Pseudo-Euclidean Space.- Geometry of?IV(2.

Harmonic maps are solutions to a natural geometrical variational prob lem. Harmonic maps are also closely related to holomorphic maps in several. Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions.

Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear Cited by: The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions.

It then presents a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak by: The harmonic map equations for unit vector fields are discussed for the particular case of Reeb fields in contact metric geometry.

It is always a harmonic vector field and it is a harmonic map under appropriate conditions on the coefficients determining the fixed g-natural metric, allowing one to exhibit large families of harmonic maps defined.

This book attempts to present a comprehensive survey on biharmonic submanifolds and biharmonic maps from the view points of Riemannian geometry. This book is. Harmonic maps between smooth Riemannian manifolds play a ubiquitous role in differential geometry.

Examples include geodesics viewed as maps, minimal surfaces, holomorphic maps and Abelian integrals viewed as maps to a circle. The theory of such maps has been extensively developed over the last 40 years, and has significant applications throughout.

A (smooth) map:M→N between Riemannian manifolds M and N is called harmonic if it is a critical point of the Dirichlet energy functional = ∫ ‖ ‖.This functional E will be defined precisely below—one way of understanding it is to imagine that M is made of rubber and N made of marble (their shapes given by their respective metrics), and that the map:M→N prescribes how one.

GEOMETRY OF HARMONIC MAPS | In these days, I have started working on the theory of Harmonic maps on Riemannian and semi-Riemannian manifolds.

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 Rating: % positive.

Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics.

In Riemannian geometry, a branch of mathematics, harmonic coordinates are a coordinate system (x 1,x n) on a Riemannian manifold each of whose coordinate functions x i is harmonic, meaning that it satisfies Laplace's equation = Here Δ is the Laplace–Beltrami lently, regarding a coordinate system as a local diffeomorphism φ: M → R n.

The last two chapters treat the variational problem on the energy of maps between two Riemannian manifolds and its solution, harmonic maps. The concept of a harmonic map includes geodesics and minimal submanifolds as examples. Its existence and properties have successfully been applied to various problems in geometry and topology.

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.

Wood, open the proceedings. Harmonic maps are generalisations of the concept of geodesics. They encompass many fundamental examples in differential geometry and have recently become of widespread use in many areas of mathematics and mathematical : Martin A.

Guest. I would recommend Jost's book "Riemannian geometry and geometric analysis" as well as Sharpe's "Differential geometry". The first book is pragmatically written and guides the reader to a lot of interesting stuff, like Hodge's theorem, Morse homology and harmonic maps.

The second book is mainly concerned with Cartan connection, but before that. It is the aim of this book to be a systematic and comprehensive introduction to Riemannian geometry and a representative introduction to the methods of geometric analysis. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds.

75 Harmonic Maps into Manifolds of Nonpositive Sectional Curvature. /5(1). Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange. 53B21, 53L20, 32C17, 35I60, XX, 58E20, 57R15 Riemannian geometry Riemannian manifolds Lie groups symplectic geometry vector bundles Laplace operator harmonic functions harmonic maps curvature Dirac operator geometry of submanifolds geodesics Jacobi fields symmetric spaces Kähler manifolds Morse theory Floer homology quantum field theory.

The 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.Hermitian harmonic maps plex structure we can always choose eA such that feAg = fe1;e2; ;em; Je1;Je2; ; complex unitary frame will be fE ;E g satis- fying e = E + E, Je = p1 −1 (E − E) and that fE g spans the complex tangent spaces T0(M) locally.

Let N be a Riemannian manifold of real dimension n, and let u be a smooth map from M to we always choose .