Differential Geometry

Cartan's Generalization of Klein's Erlangen Program

Author: R.W. Sharpe

Publisher: Springer Science & Business Media

ISBN: 9780387947327

Category: Mathematics

Page: 426

View: 6766

Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces généralisés" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.

Using the Mathematics Literature

Author: Kristine K. Fowler

Publisher: CRC Press

ISBN: 9780824750350

Category: Language Arts & Disciplines

Page: 475

View: 7979

This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

Differential Geometry and Its Applications

Proceedings of the 10th International Conference, DGA 2007, Olomouc, Czech Republic, 27-31 August 2007

Author: N.A

Publisher: World Scientific

ISBN: 9812790616

Category: Electronic books

Page: 732

View: 1618

This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture OC Leonhard Euler OCo 300 years onOCO by R Wilson. Notable contributors include J F Cariena, M Castrilln Lpez, J Erichhorn, J-H Eschenburg, I KoliO, A P Kopylov, J Korbai, O Kowalski, B Kruglikov, D Krupka, O Krupkovi, R L(r)andre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Muoz Masqu(r), S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slovik, J Szilasi, L Tamissy, P Walczak, and others."

An Alternative Approach to Lie Groups and Geometric Structures

Author: Ercüment Ortaçgil

Publisher: Oxford University Press

ISBN: 0192554840

Category: Mathematics

Page: 240

View: 989

This book presents a new and innovative approach to Lie groups and differential geometry. Rather than compiling and reviewing the existing material on this classical subject, Professor Ortaçgil instead questions the foundations of the subject, and proposes a new direction. Aimed at the curious and courageous mathematician, this book aims to provoke further debate and inspire further development of this original research.

Conformal Differential Geometry

Q-Curvature and Conformal Holonomy

Author: Helga Baum,Andreas Juhl

Publisher: Springer Science & Business Media

ISBN: 3764399090

Category: Mathematics

Page: 152

View: 7776

Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.

Conformal Differential Geometry and Its Generalizations

Author: Maks A. Akivis,Maks Aĭzikovich Akivis,Vladislav V. Goldberg,Vladislav Viktorovich Goldberg

Publisher: John Wiley & Sons

ISBN: 9780471149583

Category: Mathematics

Page: 383

View: 4508

Comprehensive coverage of the foundations, applications, recentdevelopments, and future of conformal differential geometry Conformal Differential Geometry and Its Generalizations is thefirst and only text that systematically presents the foundationsand manifestations of conformal differential geometry. It offersthe first unified presentation of the subject, which wasestablished more than a century ago. The text is divided into sevenchapters, each containing figures, formulas, and historical andbibliographical notes, while numerous examples elucidate thenecessary theory. Clear, focused, and expertly synthesized, Conformal DifferentialGeometry and Its Generalizations * Develops the theory of hypersurfaces and submanifolds of anydimension of conformal and pseudoconformal spaces. * Investigates conformal and pseudoconformal structures on amanifold of arbitrary dimension, derives their structure equations,and explores their tensor of conformal curvature. * Analyzes the real theory of four-dimensional conformal structuresof all possible signatures. * Considers the analytic and differential geometry of Grassmann andalmost Grassmann structures. * Draws connections between almost Grassmann structures and webtheory. Conformal differential geometry, a part of classical differentialgeometry, was founded at the turn of the century and gave rise tothe study of conformal and almost Grassmann structures in lateryears. Until now, no book has offered a systematic presentation ofthe multidimensional conformal differential geometry and theconformal and almost Grassmann structures. After years of intense research at their respective universitiesand at the Soviet School of Differential Geometry, Maks A. Akivisand Vladislav V. Goldberg have written this well-conceived,expertly executed volume to fill a void in the literature. Dr.Akivis and Dr. Goldberg supply a deep foundation, applications,numerous examples, and recent developments in the field. Many ofthe findings that fill these pages are published here for the firsttime, and previously published results are reexamined in a unifiedcontext. The geometry and theory of conformal and pseudoconformal spaces ofarbitrary dimension, as well as the theory of Grassmann and almostGrassmann structures, are discussed and analyzed in detail. Thetopics covered not only advance the subject itself, but poseimportant questions for future investigations. This exhaustive,groundbreaking text combines the classical results and recentdevelopments and findings. This volume is intended for graduate students and researchers ofdifferential geometry. It can be especially useful to thosestudents and researchers who are interested in conformal andGrassmann differential geometry and their applications totheoretical physics.


Author: Reinhold Remmert

Publisher: N.A

ISBN: 9783540553847

Category: Functions of complex variables

Page: 299

View: 7805

Diese dritte Auflage wurde zusammen mit dem zweitgenannten Autor kritisch durchgesehen, ergnzt und verbessert. Ein weiteres Kapitel ber geometrische Funktionentheorie und schlichte Funktionen enthlt einen Beweis der Bieberbachschen Vermutung. Der ... vorliegende zweite Band der Funktionentheorie erfllt voll die Erwartungen, die der erste Band geweckt hat. Wieder beeindrucken vor allem die hochinteressanten historischen Bemerkungen zu den einzelnen Themenkreisen, als besonderer Leckerbissen wird das Gutachten von Gau ber Riemanns Dissertation vorgestellt... Jedes einzelne Kapitel enthlt ausfhrliche Literaturangaben. Ferner werden oft sehr aufschlussreiche Hinweise auf die Funktionentheorie mehrerer Vernderlicher gegeben. Die vielen Beispiele und bungsaufgaben bilden eine wertvolle Ergnzung der brillant dargelegten Theorie. Der Rezensent bedauert, dass ihm nicht schon als Student ein derartig umfassendes, qualitativ hochstehendes Lehrbuch zur Verfgung stand." Monatshefte fr Mathematik

Differential Manifolds

Author: Antoni A. Kosinski

Publisher: Academic Press

ISBN: 9780080874586

Category: Mathematics

Page: 248

View: 4091

Differential Manifolds is a modern graduate-level introduction to the important field of differential topology. The concepts of differential topology lie at the heart of many mathematical disciplines such as differential geometry and the theory of lie groups. The book introduces both the h-cobordism theorem and the classification of differential structures on spheres. The presentation of a number of topics in a clear and simple fashion make this book an outstanding choice for a graduate course in differential topology as well as for individual study. Presents the study and classification of smooth structures on manifolds It begins with the elements of theory and concludes with an introduction to the method of surgery Chapters 1-5 contain a detailed presentation of the foundations of differential topology--no knowledge of algebraic topology is required for this self-contained section Chapters 6-8 begin by explaining the joining of manifolds along submanifolds, and ends with the proof of the h-cobordism theory Chapter 9 presents the Pontriagrin construction, the principle link between differential topology and homotopy theory; The final chapter introduces the method of surgery and applies it to the classification of smooth structures on spheres

Vorlesungen über Differentialgeometrie und geometrische Grundlagen von Einsteins Relativitätstheorie I

Elementare Differentialgeometrie

Author: Wilhelm Blaschke,Gerhard Thomsen

Publisher: Springer-Verlag

ISBN: 3662429438

Category: Mathematics

Page: 314

View: 7318

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Differentialgeometrie, Topologie und Physik

Author: Mikio Nakahara

Publisher: Springer-Verlag

ISBN: 3662453002

Category: Science

Page: 597

View: 4440

Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

Vorlesungen über die Theorie der algebraischen Zahlen

Author: Erich Hecke

Publisher: University of Pennsylvania Press

ISBN: 9780821821435

Category: Mathematics

Page: 274

View: 4419

This title has been described as An elegant and comprehensive account of the modern theory of algebraic numbers - Bulletin of the AMS.

Geometrie der Berührungstransformationen

Author: Sophus Lie,Georg Scheffers

Publisher: American Mathematical Soc.

ISBN: 9780821837795

Category: Mathematics

Page: 693

View: 8138

The Geometry of Contact Transformation, Sophus Lie's final work.