By Gregor Fels

ISBN-10: 0817643915

ISBN-13: 9780817643911

This monograph, divided into 4 components, offers a finished therapy and systematic exam of cycle areas of flag domain names. Assuming just a uncomplicated familiarity with the suggestions of Lie idea and geometry, this paintings provides an entire constitution idea for those cycle areas, in addition to their purposes to harmonic research and algebraic geometry. Key gains: * obtainable to readers from a variety of fields, with all of the precious heritage fabric supplied for the nonspecialist * Many new effects awarded for the 1st time * pushed by way of a number of examples * The exposition is gifted from the complicated geometric standpoint, however the equipment, functions and masses of the inducement additionally come from genuine and complicated algebraic teams and their representations, in addition to different parts of geometry * Comparisons with classical Barlet cycle areas are given * reliable bibliography and index. Researchers and graduate scholars in differential geometry, complicated research, harmonic research, illustration idea, transformation teams, algebraic geometry, and components of worldwide geometric research will take advantage of this paintings.

By Michèle Audin

ISBN-10: 3764321768

ISBN-13: 9783764321765

The cloth and references during this prolonged moment version of "The Topology of Torus activities on Symplectic Manifolds", released as quantity ninety three during this sequence in 1991, were up-to-date. Symplectic manifolds and torus activities are investigated, with various examples of torus activities, for example on a few moduli areas. even though the e-book continues to be headquartered on convexity effects, it comprises even more fabric, specifically plenty of new examples and routines.

By J. Eells, B. Fuglede, M. Gromov

ISBN-10: 0521773113

ISBN-13: 9780521773119

This research-level monograph on harmonic maps among singular areas units out a lot new fabric at the concept, bringing all of the study jointly for the 1st time in a single position. Riemannian polyhedra are a category of such areas which are specially compatible to function the area of definition for harmonic maps. Their houses are thought of intimately, with many examples being given, and strength concept on Riemmanian polyhedra is usually thought of. The paintings will function a concise resource and reference for all researchers operating during this box or the same one.

By Maks A. Akivis, Vladislav V. Goldberg

ISBN-10: 0387404635

ISBN-13: 9780387404639

During this e-book the authors learn the differential geometry of types with degenerate Gauss maps. They use the most tools of differential geometry, particularly, the tools of relocating frames and external differential varieties in addition to tensor tools. via those tools, the authors notice the constitution of sorts with degenerate Gauss maps, ensure the singular issues and singular types, locate focal pictures and build a type of the kinds with degenerate Gauss maps.The authors introduce the above pointed out equipment and follow them to a sequence of concrete difficulties bobbing up within the thought of types with degenerate Gauss maps. What makes this e-book designated is the authors' use of a scientific program of tools of projective differential geometry besides equipment of the classical algebraic geometry for learning forms with degenerate Gauss maps. This e-book is meant for researchers and graduate scholars drawn to projective differential geometry and algebraic geometry and their functions. it may be used as a textual content for complicated undergraduate and graduate scholars. either authors have released over a hundred papers every one. each one has written a few books, together with Conformal Differential Geometry and Its Generalizations (Wiley 1996), Projective Differential Geometry of Submanifolds (North-Holland 1993), and Introductory Linear Algebra (Prentice-Hall 1972), that have been written by means of them together.

By V.I. Arnold, A.N. Varchenko, S.M. Gusein-Zade

ISBN-10: 1461239400

ISBN-13: 9781461239406

ISBN-10: 1461284082

ISBN-13: 9781461284086

The current. quantity is the second one quantity of the publication "Singularities of Differentiable Maps" by way of V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. the 1st quantity, subtitled "Classification of severe issues, caustics and wave fronts", was once released by means of Moscow, "Nauka", in 1982. it will likely be talked about during this textual content easily as "Volume 1". when the 1st quantity contained the zoology of differentiable maps, that's it was once dedicated to an outline of what, the place and the way singularities can be encountered, this quantity comprises the weather of the anatomy and body structure of singularities of differentiable features. which means the questions thought of in it are in regards to the constitution of singularities and the way they functionality. one other virtue of the current quantity is that we take a difficult examine questions for which you will need to paintings within the advanced area, the place the 1st quantity used to be dedicated to subject matters for which, most of the time, it was once no longer very important which box (real or complicated) we have been contemplating. Such subject matters as, for instance, decomposition of singularities, the relationship among singularities and Lie algebras and the asymptotic behaviour of alternative integrals looking on parameters develop into clearer within the advanced area. The e-book comprises 3 elements. within the first half we reflect on the topological constitution of remoted serious issues of holomorphic features. We describe the elemental topological features of such severe issues: vanishing cycles, unusual bases, intersection matrices, monodromy teams, the adaptation operator and their interconnections and approach to calculation.

By Joseph C. Varilly

ISBN-10: 3037190248

ISBN-13: 9783037190241

Noncommutative geometry, encouraged by way of quantum physics, describes singular areas by way of their noncommutative coordinate algebras and metric constructions through Dirac-like operators. Such metric geometries are defined mathematically by means of Connes' idea of spectral triples. those lectures, introduced at an EMS summer time college on noncommutative geometry and its purposes, offer an outline of spectral triples in response to examples. This advent is aimed toward graduate scholars of either arithmetic and theoretical physics. It bargains with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, motion functionals, and isospectral deformations. The structural framework is the idea that of a noncommutative spin geometry; the stipulations on spectral triples which ensure this idea are constructed intimately. The emphasis all through is on gaining realizing through computing the main points of particular examples. The publication presents a center flooring among a accomplished textual content and a narrowly centred examine monograph. it truly is meant for self-study, allowing the reader to achieve entry to the necessities of noncommutative geometry. New good points because the unique direction are an elevated bibliography and a survey of newer examples and functions of spectral triples. A e-book of the ecu Mathematical Society (EMS). dispensed in the Americas through the yankee Mathematical Society.

By Chao K.C., Robinson R.L. (eds.)

ISBN-10: 0841205000

ISBN-13: 9780841205000

By Jost-Hinrich Eschenburg, Jürgen Jost

ISBN-10: 3642385214

ISBN-13: 9783642385216

ISBN-10: 3642385222

ISBN-13: 9783642385223

Das vorliegende Lehrbuch bietet eine moderne Einführung in die Differenzialgeometrie - etwa im Umfang einer einsemestrigen Vorlesung. Zunächst behandelt es die Geometrie von Flächen im Raum. Viele Beispiele schulen Leser in geometrischer Anschauung, deren wichtigste Klasse die Minimalflächen bilden. Zu ihrem Studium entwickeln die Autoren analytische Methoden und lösen in diesem Zusammenhang das Plateausche challenge. Es besteht darin, eine Minimalfläche mit vorgegebener Berandung zu finden. Als Beispiel einer globalen Aussage der Differenzialgeometrie beweisen sie den Bernsteinschen Satz. Weitere Kapitel behandeln die innere Geometrie von Flächen einschließlich des Satzes von Gauss-Bonnet, und stellen die hyperbolische Geometrie ausführlich dar. Die Autoren verknüpfen geometrische Konstruktionen und analytische Methoden und folgen damit einem zentralen pattern der modernen mathematischen Forschung. Verschiedene geistesgeschichtliche Bemerkungen runden den textual content ab. Die Neuauflage wurde überarbeitet und aktualisiert.

By Ilya J. Bakelman

ISBN-10: 0824788974

ISBN-13: 9780824788971

This reference positive aspects papers from the precise consultation of the yankee Mathematical Society assembly held in 1990 on the college of North Texas, Denton - discussing and constructing examine on boundary worth difficulties for nonlinear partial differential equations and comparable problems.;Written through greater than 15 specialists within the box, Geometric research and Nonlinear Partial Differential Equations: provides equipment and result of the convex our bodies and geometric inequalities idea and its functions to differential equations, geometry, and mathematical physics; information contemporary stories on Monge-Ampere equations, emphasizing geometric inequalities governing a priori estimates of suggestions and lifestyles theorems of the Dirichlet challenge for convex generalized ideas and displaying the proofs of all theorems; examines the generalization of the isoperimetric inequality for two-dimensional common convex surfaces whose necessary Gaussian curvature is lower than 2 pi; and comprises open difficulties at the concept of surfaces with consistent suggest curvature.;Geometric research and Nonlinear Partial Differential Equations is for mathematical analysts, geometers, natural and utilized mathematicians, physicists, engineers, machine scientists, and upper-level undergraduate and graduate scholars in those disciplines.

By Marcos M. Alexandrino

ISBN-10: 3319166123

ISBN-13: 9783319166124

ISBN-10: 3319166131

ISBN-13: 9783319166131

This publication offers easy accessibility to the speculation of Lie teams and isometric activities on tender manifolds, utilizing a concise geometric strategy. After a gradual advent to the topic, a few of its contemporary functions to lively examine components are explored, protecting a continuing reference to the fundamental fabric. the subjects mentioned comprise polar activities, singular Riemannian foliations, cohomogeneity one activities, and definitely curved manifolds with many symmetries. This ebook stems from the adventure accumulated via the authors in different lectures alongside the years and was once designed to be as self-contained as attainable. it really is meant for complex undergraduates, graduate scholars and younger researchers in geometry and will be used for a one-semester direction or self sufficient study.