This volume highlights some of the current interests of researchers working at the interface between string theory and algebraic geometry. The topics covered include manifolds of special holonomy, supergravity, supersymmetry, D-branes, the McKay correspondence and the Fourier-Mukai transform.
This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechanics, gauge fields theories, relativity and gravitation. The order of presentation corresponds to that used for the relevant material in theoretical physics: the geometry of affine spaces, which is appropriate to special relativity theory, as well as to Newtonian mechanics, is developed in the first half of the book, and the geometry of manifolds, which is needed for general relativity and gauge field theory, in the second half.
The object of this book is to introduce the reader to some of the most important techniques of modern global geometry. In writing it we had in mind the beginning graduate student willing to specialize in this very challenging field of mathematics. The necessary prerequisite is a good knowledge of the calculus with several variables, linear algebra and some elementary point-set topology.
Riemannian Geometry of Contact and Symplectic Manifolds, 2 Edition
Second Edition features new material in most chapters, but particularly in Chapters 3, 7, and 12 Covers major new topics, such as a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle Features improvements and general corrections based off of the first edition throughout the text Intended for a broad audience of mathematicians, researchers and students in Riemannian geometry
This graduate level textbook offers graduate students a rapid introduction to the language of the subject of ordinary differential equations followed by a careful treatment of the central topics of the qualitative theory. In addition, special attention is given to the origins and applications of differential equations in physical science and engineering. Of special interest to mathematics students is a multifaceted approach to existence theory, for solutions and for invariant manifolds....
