Harmonic Morphisms Between Riemannian Manifolds PDF Download
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Author: Paul Baird
Publisher: Oxford University Press
ISBN: 9780198503620
Category : Mathematics
Languages : en
Pages : 540
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Book Description
This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Author: Paul Baird
Publisher: Oxford University Press
ISBN: 9780198503620
Category : Mathematics
Languages : en
Pages : 540
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Book Description
This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Author: S. R. Sario
Publisher: Springer
ISBN: 354037261X
Category : Mathematics
Languages : en
Pages : 518
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Book Description
Author: James Eells
Publisher: World Scientific
ISBN: 9789810214661
Category : Mathematics
Languages : en
Pages : 38
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Book Description
Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, å-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Khlerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.
Author: Yuri Kifer
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
Author: James Eells
Publisher: Cambridge University Press
ISBN: 9780521773119
Category : Mathematics
Languages : en
Pages : 316
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Book Description
A research level book on harmonic maps between singular spaces, by renowned authors, first published in 2001.
Author: Tiffany Lynn Troutman
Publisher:
ISBN:
Category : Harmonic functions
Languages : en
Pages : 90
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Book Description
Author: Werner Ballmann
Publisher:
ISBN:
Category :
Languages : de
Pages : 13
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Book Description
Author: Hyeong In Choi
Publisher:
ISBN:
Category :
Languages : en
Pages : 156
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Book Description
Author: Yuanlong Xin
Publisher: Springer Science & Business Media
ISBN: 1461240840
Category : Mathematics
Languages : en
Pages : 252
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Book Description
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, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems.
Author: W. V. D. Hodge
Publisher: CUP Archive
ISBN: 9780521358811
Category : Mathematics
Languages : en
Pages : 308
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Book Description
First published in 1941, this book, by one of the foremost geometers of his day, rapidly became a classic. In its original form the book constituted a section of Hodge's essay for which the Adam's prize of 1936 was awarded, but the author substantially revised and rewrote it. The book begins with an exposition of the geometry of manifolds and the properties of integrals on manifolds. The remainder of the book is then concerned with the application of the theory of harmonic integrals to other branches of mathematics, particularly to algebraic varieties and to continuous groups. Differential geometers and workers in allied subjects will welcome this reissue both for its lucid account of the subject and for its historical value. For this paperback edition, Professor Sir Michael Atiyah has written a foreword that sets Hodges work in its historical context and relates it briefly to developments.
