Category: Differential Geometry

By Michel Demazure

Based on a lecture path, this article provides a rigorous creation to nonlinear research, dynamical platforms and bifurcation concept together with disaster idea. at any place applicable it emphasizes a geometric or coordinate-free method permitting a transparent concentrate on the basic mathematical constructions. It brings out beneficial properties universal to various branches of the topic whereas giving considerable references for extra complex or technical developments.

By Mikio Nakahara

This booklet introduces a number of present mathematical the way to postgraduate scholars of theoretical physics. this can be accomplished through featuring functions of the math to physics, high-energy physics, common relativity and condensed subject physics

By Pedro de M. Rios, Eldar Straume

In mathematical physics, the correspondence among quantum and classical mechanics is a principal subject, which this publication explores in additional element within the specific context of spin platforms, that's, SU(2)-symmetric mechanical platforms. a close presentation of quantum spin-j structures, with emphasis at the SO(3)-invariant decomposition in their operator algebras, is first by means of an advent to the Poisson algebra of the classical spin approach after which by way of a equally targeted exam of its SO(3)-invariant decomposition. The publication subsequent proceeds with a close and systematic learn of basic quantum-classical image correspondences for spin-j platforms and their brought about twisted items of services at the 2-sphere. This unique systematic presentation culminates with the learn of twisted items within the asymptotic restrict of excessive spin numbers. within the context of spin structures it exhibits how classical mechanics might or would possibly not become an asymptotic restrict of quantum mechanics. The e-book could be a invaluable advisor for researchers during this box and its self-contained strategy additionally makes it a precious source for graduate scholars in arithmetic and physics.

By Lizhen Ji; Scott A Wolpert; Shing-Tung Yau

By Jean Dieudonné

A vintage to be had back! This e-book lines the background of algebraic topology starting with its construction by means of Henry Poincaré in 1900, and describing intimately the $64000 principles brought within the conception sooner than 1960. In its first thirty years the sector appeared restricted to functions in algebraic geometry, yet this replaced dramatically within the Nineteen Thirties with the production of differential topology through Georges De Rham and Elie Cartan and of homotopy idea via Witold Hurewicz and Heinz Hopf. The effect of topology started to unfold to progressively more branches because it steadily took on a principal position in arithmetic. Written by way of a world-renowned mathematician, this booklet will make intriguing studying for a person operating with topology.

By Yu.G. Reshetnyak, Yu.G. Reshetnyak, E. Primrose, V.N. Berestovskij, I.G. Nikolaev

This quantity of the Encyclopaedia comprises articles, which offer a survey of contemporary examine into non-regular Riemannian geometry, conducted more often than not through Russian mathematicians. the 1st article written through Reshetnyak is dedicated to the speculation of two-dimensional Riemannian manifolds of bounded curvature. techniques of Riemannian geometry, akin to the realm and quintessential curvature of a collection, and the size and crucial curvature of a curve also are outlined for those manifolds. a few basic result of Riemannian goemetry just like the Gauss-Bonnet formulation are precise within the extra common case thought of within the e-book. the second one article via 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 themes, that have no longer but been taken care of in monograph shape. accordingly the publication may be immensely beneficial to graduate scholars and researchers in geometry, particularly Riemannian geometry.

By Rajeev S.G.

By L. Tamássy, J. Szenthe

This quantity includes thirty-six learn articles offered at the Colloquium on Differential Geometry, which used to be held in Debrecen, Hungary, July 26-30, 1994. The convention was once a continuation in the sequence of the Colloquia of the J?nos Bolyai Society. the variety lined displays present task in differential geometry. the most issues are Riemannian geometry, Finsler geometry, submanifold thought and functions to theoretical physics. comprises numerous fascinating effects through best researchers in those fields: e.g. on non-commutative geometry, spin bordism teams, Cosserat continuum, box theories, moment order differential equations, sprays, normal operators, larger order body bundles, Sasakian and K?hler manifolds. viewers: This booklet should be invaluable for researchers and postgraduate scholars whose paintings comprises differential geometry, international research, research on manifolds, relativity and gravitation and electromagnetic thought.

By Dariusz Chruscinski, Andrzej Jamiolkowski

This paintings examines the attractive and significant actual proposal referred to as the 'geometric phase,' bringing jointly diversified actual phenomena less than a unified mathematical and actual scheme.

Several well-established geometric and topological tools underscore the mathematical therapy of the topic, emphasizing a coherent viewpoint at a slightly subtle point. what's targeted during this textual content is that either the quantum and classical levels are studied from a geometrical perspective, supplying worthy insights into their courting that experience now not been formerly emphasised on the textbook point.

Key themes and contours:

• historical past fabric provides simple mathematical instruments on manifolds and differential varieties.

• Topological invariants (Chern sessions and homotopy thought) are defined in uncomplicated and urban language, with emphasis on actual purposes.

• Berry's adiabatic section and its generalization are brought.

• Systematic exposition treats diversified geometries (e.g., symplectic and metric buildings) residing on a quantum part house, in reference to either abelian and nonabelian stages.

• Quantum mechanics is gifted as classical Hamiltonian dynamics on a projective Hilbert area.

• Hannay’s classical adiabatic section and angles are explained.

• assessment of Berry and Robbins' progressive method of spin-statistics.

• A bankruptcy on Examples and functions paves the way in which for ongoing experiences of geometric stages.

• difficulties on the finish of every bankruptcy.

• prolonged bibliography and index.

Graduate scholars in arithmetic with a few past wisdom of quantum mechanics will find out about a category of functions of differential geometry and geometric tools in quantum conception. Physicists and graduate scholars in physics will research ideas of differential geometry in an utilized context.

By Leonard S. Charlap

Many arithmetic books be afflicted by schizophrenia, and this is often another. at the one hand it attempts to be a reference for the fundamental effects on flat riemannian manifolds. however it makes an attempt to be a textbook that are used for a moment 12 months graduate direction. My objective was once to maintain the second one character dominant, however the reference personality stored breaking out particularly on the finish of sections within the kind of comments that include extra complex fabric. to meet this reference personality, i'm going to commence by means of telling you a bit in regards to the subject material of the e-book, after which i will speak about the textbook point. A flat riemannian manifold is an area within which you could discuss geometry (e. g. distance, perspective, curvature, "straight lines," and so forth. ) and, additionally, the geometry is in the neighborhood the only we know and love, specifically euclidean geometry. which means close to any element of this area you may introduce coordinates in order that with recognize to those coordinates, the principles of euclidean geometry carry. those coordinates should not legitimate within the complete area, so that you cannot finish the distance is euclidean area itself. during this publication we're customarily serious about compact flat riemannian manifolds, and until we are saying differently, we use the time period "flat manifold" to intend "compact flat riemannian manifold. " It seems that crucial invariant for flat manifolds is the basic group.