Ricci Flow and the Poincare Conjecture
by John Morgan, Gang Tian
Publisher: American Mathematical Society 2007
Number of pages: 493
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's three preprints. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
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by Brian White - arXiv
The goal was to give beginning graduate students an introduction to some of the most important basic facts and ideas in minimal surface theory. Prerequisites: the reader should know basic complex analysis and elementary differential geometry.
by Ivan Kolar, Peter W. Michor, Jan Slovak - Springer
A comprehensive textbook on all basic structures from the theory of jets. It begins with an introduction to differential geometry. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces.
by Gerald Jay Sussman, Jack Wisdom - MIT
Differential geometry is deceptively simple. It is surprisingly easy to get the right answer with informal symbol manipulation. We use computer programs to communicate a precise understanding of the computations in differential geometry.
by J.L. Koszul - Tata Institute of Fundamental Research
From the table of contents: Differential Calculus; Differentiable Bundles; Connections on Principal Bundles; Holonomy Groups; Vector Bundles and Derivation Laws; Holomorphic Connections (Complex vector bundles, Almost complex manifolds, etc.).