By Wilhelm Klingenberg (auth.)
This English variation might function a textual content for a primary 12 months graduate path on differential geometry, as did for a very long time the Chicago Notes of Chern pointed out within the Preface to the German version. appropriate references for ordin ary differential equations are Hurewicz, W. Lectures on traditional differential equations. MIT Press, Cambridge, Mass., 1958, and for the topology of surfaces: Massey, Algebraic Topology, Springer-Verlag, big apple, 1977. Upon David Hoffman fell the tough activity of remodeling the tightly built German textual content into one that may mesh good with the extra comfy layout of the Graduate Texts in arithmetic sequence. There are a few e1aborations and several other new figures were further. I belief that the benefits of the German variation have survived while even as the efforts of David helped to explain the final belief of the path the place we attempted to place Geometry ahead of Formalism with no giving up mathematical rigour. 1 desire to thank David for his paintings and his enthusiasm through the entire interval of our collaboration. whilst i want to commend the editors of Springer-Verlag for his or her endurance and solid suggestion. Bonn Wilhelm Klingenberg June,1977 vii From the Preface to the German version This e-book has its origins in a one-semester direction in differential geometry which 1 have given again and again at Gottingen, Mainz, and Bonn.
By A. Y. Khinchin
Mathematicians with a easy realizing of quantum physics and physicists attracted to the subject will make the most of this functional textual content. The therapy examines the foundation of quantum statistical computational equipment, the selection of the suggest values of profession numbers, the principles of the information of photons and fabric debris, and statistical thermodynamics. 1960 variation.
By Mikio Nakahara
Differential geometry and topology became crucial instruments for plenty of theoretical physicists. particularly, they're fundamental in theoretical stories of condensed topic physics, gravity, and particle physics. Geometry, Topology and Physics, moment variation introduces the guidelines and strategies of differential geometry and topology at a degree appropriate for postgraduate scholars and researchers in those fields. the second one version of this well known and confirmed textual content includes a variety of alterations designed to satisfy the wishes of the reader and replicate the advance of the topic. The e-book incorporates a significantly extended first bankruptcy, reviewing elements of direction indispensable quantization and gauge theories. bankruptcy 2 introduces the mathematical thoughts of maps, vector areas, and topology. the subsequent chapters specialize in extra complicated ideas in geometry and topology and talk about the appliance of those suggestions to liquid crystals, superfluid helium, common relativity, and bosonic string idea. Later chapters unify geometry and topology, exploring fiber bundles, attribute periods, and index theorems. New to this moment variation is the facts of the index theorem by way of supersymmetric quantum mechanics. the ultimate chapters are dedicated to the main attention-grabbing functions of geometry and topology in modern physics, particularly the research of anomalies in gauge box theories and the research of Polakov's bosonic string conception from the geometrical perspective. Geometry, Topology and Physics, moment version is a perfect advent to differential geometry and topology for postgraduate scholars and researchers in theoretical and mathematical physics.
By K. Bleuler, H. R. Petry, A. Reetz
By Jean-Paul Brasselet, Maria Aparecida Soares Ruas
The S??o Carlos Workshop on actual and intricate Singularities is the longest working workshop in singularities. it truly is held each years and is a key overseas occasion for individuals operating within the box. This quantity includes papers awarded on the 8th workshop, held on the IML, Marseille, July 19-23, 2004.
The workshop deals the chance to set up the cutting-edge and to provide new developments, new principles and new ends up in all the branches of singularities - mirrored via the contributions during this ebook: equisingularity of units and mappings, geometry of singular complicated analytic units, singularities of mappings, attribute periods, class of singularities, interplay of singularity concept with a number of the new rules in algebraic geometry imported from theoretical physics, functions of singularity idea to geometry of surfaces in low dimensional euclidean areas, to differential equations and to bifurcation theory.
By Michael Atiyah
Professor Atiyah is without doubt one of the maximum dwelling mathematicians and is celebrated during the mathematical global. he's a recipient of the Fields Medal, the mathematical similar of the Nobel Prize, and remains to be on the top of his occupation. His large variety of released papers, targeting the parts of algebraic geometry and topology, have the following been gathered into six volumes, divided thematically for simple reference through members attracted to a specific topic. Volumes III and IV hide papers written in 1963-84 and are the results of a protracted collaboration with I. M. Singer at the Index concept of elliptic operators
By Phillip Griffiths, Daniel Grossman, Visit Amazon's Robert L. Bryant Page, search results, Learn about Author Central, Robert L. Bryant,
This well timed synthesis of partial differential equations and differential geometry could be of primary value to either scholars and skilled researchers operating in geometric analysis.
By Alexander I. Bobenko, Ulrich Eitner (eds.)
This publication brings jointly diverse branches of arithmetic: the speculation of Painlevé and the speculation of surfaces. Self-contained introductions to either those fields are awarded. it truly is proven how a few classical difficulties in floor concept might be solved utilizing the fashionable thought of Painlevé equations. specifically, a vital a part of the e-book is dedicated to Bonnet surfaces, i.e. to surfaces owning households of isometries keeping the suggest curvature functionality. a world class of Bonnet surfaces is given utilizing either constituents of the speculation of Painlevé equations: the idea of isomonodromic deformation and the Painlevé estate. The ebook is illustrated through plots of surfaces. it really is meant for use by way of mathematicians and graduate scholars attracted to differential geometry and Painlevé equations. Researchers operating in a single of those components can familiarize yourself with one other appropriate department of arithmetic.
By Yu.G. Reshetnyak, Yu.G. Reshetnyak, E. Primrose, V.N. Berestovskij, I.G. Nikolaev
This quantity of the Encyclopaedia includes articles, which provide a survey of contemporary learn into non-regular Riemannian geometry, conducted regularly by way of Russian mathematicians. the 1st article written by way of Reshetnyak is dedicated to the speculation of two-dimensional Riemannian manifolds of bounded curvature. innovations of Riemannian geometry, equivalent to the realm and crucial curvature of a collection, and the size and quintessential curvature of a curve also are outlined for those manifolds. a few primary result of Riemannian goemetry just like the Gauss-Bonnet formulation are precise within the extra normal case thought of within the publication. the second one article by means of Berestovskij and Nikolaev is dedicated to the speculation of metric areas whose curvature lies among given constants. the most result's that those areas are in reality Riemannian. This end result has very important purposes in international Riemannian geometry. either components conceal issues, that have no longer but been taken care of in monograph shape. as a result the e-book might be immensely invaluable to graduate scholars and researchers in geometry, specifically Riemannian geometry.