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 Alexander I. Bobenko (ed.) - Springer
This is the book on a newly emerging field of discrete differential geometry. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics.
by Sigmundur Gudmundsson - Lund University
These notes introduce the beautiful theory of Gaussian geometry i.e. the theory of curves and surfaces in three dimensional Euclidean space. The text is written for students with a good understanding of linear algebra and real analysis.
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.).
by Peter J. Cameron - Queen Mary College
The author is concerned with the geometry of incidence of points and lines, over an arbitrary field, and unencumbered by metrics or continuity (or even betweenness). The treatment of these themes blends the descriptive with the axiomatic.