2 edition of **Harmonic maps into homogeneous spaces** found in the catalog.

Harmonic maps into homogeneous spaces

Malcolm J. Black

- 263 Want to read
- 34 Currently reading

Published
**1990** by typescript in [s.l.] .

Written in English

**Edition Notes**

Thesis (Ph.D.)- University of Warwick, 1990.

Statement | by Malcolm J. Black. |

ID Numbers | |
---|---|

Open Library | OL20153603M |

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Price: $

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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.

Harmonic maps into homogeneous spaces. [Malcolm Black] This text considers harmonic maps in homogeneous spaces and includes chapters on homogeneous geometry, Book, Internet Resource: All Authors / Contributors: Malcolm Black.

Find more information about. 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.

This text considers harmonic maps in homogeneous spaces and includes chapters on homogeneous geometry, f-structures and f-holomorphic maps, equi-harmonic maps, classification of. Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry.

Many important advances have been Harmonic Maps Into Homogeneous Spaces book. By Malcolm Black. Edition 1st Edition. First Published eBook Published 4 May Pub.

location New by: Buy Harmonic Maps Into Homogeneous Spaces (Chapman & Hall/CRC Research Notes in Mathematics Series) on FREE SHIPPING on qualified ordersCited by: Harmonic maps into homogeneous spaces by Black, Malcolm.; Harmonic maps into homogeneous spaces book edition; First published in ; Subjects: Harmonic maps, Homogeneous spaces.

HARMONIC MAPS INTO SINGULAR SPACES AND p-ADIC SUPERRIGIDITY FOR LATTICES IN GROUPS OF RANK ONE By MIKHAIL GROMOV and RICHARD SCHOEN Introduction In Part I of this paper we develop a theory of harmonic mappings into non- homogeneous maps have degree at least one and, at most points, they must have degree equal to one.

The homogeneous maps of File Size: 4MB. 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 "applies.

Abstract. A harmonic map from a Riemannian manifold into a Grassmannian manifold is characterized by a vector bundle, a space of sections of the bundle and a Laplace operator [].This characterization can be considered a generalization of a theorem of Takahashi [].We apply our main result which generalizes a theorem of Do Carmo and Wallach [] to describe moduli spaces of special Author: Yasuyuki Nagatomo.

As its applications, a characterization of harmonic maps into any homogeneous space is given and all harmonic maps of the standard Euclidean space (Rm, g0) into a Lie group (G, h) with left.

Harmonic Maps Into Homogeneous Spaces This text considers Harmonic maps in homogeneous spaces and includes chapters on homogeneous geometry, f-structures and f-holomorphic maps, equi- Harmonic maps, classification of horizontal f-structures on flag manifolds and integrable f.

The tension field of a smooth map of an arbitrary Riemannian manifold into any homogeneous space (G/K, h) with an invariant Riemannian metric h is its applications, a characterization of harmonic maps into any homogeneous space is given and all harmonic maps of the standard Euclidean space (R m, g 0) into a Lie group (G, h) with left invariant Riemannian metric h, of the form ƒ Cited by: Harmonic Maps into Homogeneous Spaces 3 Take A2m.

The left invariant vector field A~ on Gis denoted by A~(g) = L gAand the G-invariant vector field A on G=His defined by A = ˝ gA.

It is clear that A~ is a horizontal lift vector field of A and ˇ (A~) = A. In other words, A~ and A are ˇ-related. Now we introduce some geometric aspects of Gand G=H. Howard and S.W. Wei: "Nonexistence of stable harmonic maps to and from certain homogeneous spaces and submanifolds of Euclidean space" Trans.

A.M.S. (1) (), – MathSciNet CrossRef zbMATH Google ScholarCited by: 2. This paper is about harmonic maps from closed Riemann surfaces into homogeneous spaces such as flag manifolds and loop groups.

It contains the construction of a family of new examples of harmonic maps from T2=S1×S1 into F(n) or Ω(U(n)) that are not holomorphic with respect to any almost complex structure on F(n) or Ω(U(n)), where F(n) is the quotient of U(n) by any maximal torus and Ω(u(n Cited by: 1.

Nonexistence of Stable Harmonic Maps To and From Certain Homogeneous Spaces and Submanifolds of Euclidean Space Article (PDF Available) in Transactions of. Topics in Harmonic Analysis on Homogeneous Spaces (Progress in Mathematics) 1st Edition by Sigurdur Helgason (Author) › Visit Amazon's Sigurdur Helgason Page.

Find all the books, read about the author, and more. See search results for this author. Are you an author. Cited by: A Conservation Law for Harmonic Maps () Maps of Minimum Energy () The Existence and Construction of Certain Harmonic Maps () Harmonic Maps from Surfaces to Complex Projective Spaces () Examples of Harmonic Maps from Disks to Hemispheres () Variational Theory in Fibre Bundles: Examples () Constructions Twistorielles des.

H~LEIN [13] has extended his regularity theory to cover weakly harmonic maps from surfaces into homogeneous spaces; SCI-IOEN and UHLENBECK have made similar observations.

I conjecture the partial regularity theory set forth in this paper will extend as well. 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.

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 on a compact Riemannian manifold and having a target space with a highly nontrivial geometry.

Homogeneous spaces are a particular class of manifolds that behave per con-struction very symmetrically under the action of some groups, and they can be fully reconstructed just by looking at their behaviour under curtain actions. Namely any point on the manifold is correlated pairwise to any other just by the operation of elements of the Size: KB.

Harmonic maps between singular spaces I for large balls (cf. Remark of [4]). The main technical hurdle is to obtain energy decay estimates with uniform radius and this is handled in Section 4.

Our main theorem concerns better regularity of harmonic maps. More precisely, we show that harmonic maps are Lipschitz continuous away from.

4 UNIQUENESS THEOREMS FOR HARMONIC MAPS INTO METRIC SPACES In [Me], we show that we can construct an energy minimizing map u in a homotopy class of ϕ as a limit of smooth diﬀeomorphism. Theorem 4 shows that this is the only harmonic map in its homotopy class.

The key to the proof of Theorem 4 is the analysis of the local behavior of the map u. Homogeneous spaces as coset spaces. In general, if X is a homogeneous space, and H o is the stabilizer of some marked point o in X (a choice of origin), the points of X correspond to the left cosets G/H o, and the marked point o corresponds to the coset of the identity.

M is strongly unstable. As compact isotropy irreducible homogeneous spaces have "standard" immersions into Euclidean space this allows a complete list of the strongly unstable compact irreducible symmetric spaces to be made.

Introduction. A harmonic map is a smooth map between Riemannian. Harmonic maps and biharmonic maps into compact Lie groups or compact symmetric spaces. The CR analogue of harmonic maps and biharmonic maps. Biharmonic hypersurfaces of compact symmetric spaces. Preliminaries. In this section, we prepare materials for the first and second variational formulas for the bienergy functional and biharmonic : Hajime Urakawa.

Monotonicity properties of harmonic maps into general NPC spaces Dedicated to Dick Palais on his 80th birthday Georgios Daskalopoulos1 Brown University [email protected] Chikako Mese2 Johns Hopkins University [email protected] 1 Introduction In this article, we present results about harmonic maps into general NPC spaces.

This book is an outgrowth of the nineteenth Summer Research Institute of the American Mathematical Society which was devoted to the topic Harmonic Analysis on Homogeneous Spaces. The Institute was held at Williams College in Williamstown, Massachusetts from July 31 to Augand was.

maps into the spheres Sn, η > 3, with canonical metrics of constant positive curvature. They showed in particular that, when m. "The book reflects recent trends in modern harmonic analysis on spaces of homogeneous type.

is worth being read by every analyst." (Boris Rubin, Zentralblatt MATH, Vol. ) "The book under review deals with real variable theory on spaces of homogeneous type. THE ENERGY FUNCTION AND HOMOGENEOUS HARMONIC MAPS 3 where C(adθ) is the Casimir operator of the representation adθ of g1 on is reminis-cent of the “distance function” of [2] and the “square of the norm of the moment map” kµk2 of [7], and indeed the critical point theory of these two functions turns out to be related toCited by: 2.

The specific goal of the book is to show how the theory of loop groups can be used to study harmonic maps.

By concentrating on the main ideas and examples, the author leads up Author: Martin A. Guest. Regularity of n/2-harmonic maps into spheres Armin Schikorra We prove H older continuity for n=2-harmonic maps from subsets of Rn into a sphere. This extends a recent one-dimensional result by F.

Da Lio and T. Rivi ere to arbitrary dimensions. 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 solutions.

A presentation of "exotic" functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. ON NATURALLY REDUCTIVE HOMOGENEOUS SPACES HARMONICALLY EMBEDDED INTO SPHERES GABOR TOTH 1.

Introduction and preliminaries This note continues earlier studies [9, 10] concerning rigidity properties of harmonic maps into spheres. Given a harmonic ma S",p n /: M ^ 2 - [5> ] of a compact Riemannian manifold M into the Euclidean n-sphere S" the (finite.

Harmonic Morphisms from Homogeneous Spaces - Some Existence Theory - Sigmundur Gudmundsson Department of Mathematics Faculty of Science Lund University [email protected] February 8, Harmonic Morphisms Homogeneous Spaces De nition (harmonic morphism)File Size: KB.

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups.

The theory of Lie groups involves many areas of mathematics: algebra, differential geometry, algebraic geometry, analysis, and differential equations. Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted by bundles associated to the irreducible, possibly projective, representations of H.

Here, we give a [ ]Cited by:. EXISTENCE OF HARMONIC MAPS INTO CAT(1) SPACES 3 a local removable singularity theorem for harmonic maps into a small ball. The second key idea, Theoremis a monotonicity of the area in extrinsic balls in the target space, for conformal harmonic maps from a surface to a CAT(1) space.

This theorem extends.The intent of this book is to give students of mathematics and mathematicians in diverse fields an entry into the subject of harmonic analysis on homogeneous spaces.

It is hoped that the book could be used as a supplement to a standard one-year course in Lie groups and Lie algebras or as the main text in a more unorthodox course on the subject.R.

Camporesi, Harmonic analysis and propagators on homogeneous spaces 5 results. This question arises from the remarkable property of Lie groups [45,56, ] that the Gaussian (or leading WKB) approximation to the free particle propagator is exact there.

More precisely, the propagator of a free particle on a Lie group, as well as the quantum File Size: 8MB.