Lectures on Differential Geometry

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups.This text a

This graduate textbook offers a self-contained introduction to the concepts and techniques of logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry and number theory. It features a systematic exposition of the foundations of the field, from the basic results on convex geometry and commutative monoids to the theory of logarithmic schemes and their de Rham and Betti cohomology. The book will be of use to graduate students and researchers working in algebraic, analytic, and arithmetic geometry as well as related fields.

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. It is intended to be the first in

The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity proper

The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity proper

The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geomet

This text is based on a historic approach used at MIT to teach projective geometry to junior and senior undergraduates. The author develops the geometry of plane and space, leading up to conics and qu

This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are develop

The link between the physical world and its visualization is geometry. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. The wide range of topics includes curve theory, a detailed study of surfaces, curvature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss–Bonnet theorem. The section on cartography demonstrates the concrete importance of elementary differential geometry in applications. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses

This easy-to-read, generously illustrated textbook is an elementary introduction to differential geometry with emphasis on geometric results, preparing students for more advanced study. Clearly develo

This elementary account of the differential geometry of curves and surfaces in space deals with curvature and torsion, involutes and evolutes, curves on a surface, curvature of surfaces, and developab

This is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions an

Developed from the author's course at the U. of Notre Dame, this second-edition work (the first was published in 1996) covers roughly the same material as two of the five volumes of Spivak's A Compre

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.

Synthetic Differential Geometry is a method of reasoning in differential geometry and differential calculus, based on the assumption of sufficiently many nilpotent elements on the number line, in particular numbers d such that d2=0. The use of nilpotent elements allows one to replace the limit processes of calculus by purely algebraic calculations and notions. For the first half of the book, first published in 2006, familiarity with differential calculus and abstract algebra is presupposed during the development of results in calculus and differential geometry on a purely axiomatic/synthetic basis. In the second half basic notions of category theory are presumed in the construction of suitable Cartesian closed categories and the interpretation of logical formulae within them. This is a second edition of Kock's classical text from 1981. Many notes have been included, with comments on developments in the field from the intermediate years, and almost 100 new bibliographic entries have bee