Biography[ edit ] Cheeger graduated from Harvard University with a B. He graduated from Princeton University with an M. He worked as a teaching assistant and research assistant at Princeton University from —, a National Science Foundation postdoctoral fellow and instructor from —, an assistant professor from to at the University of Michigan , and an associate professor from — at SUNY at Stony Brook. Cheeger was a professor at SUNY, Stony Brook from to , a leading professor from to , and a distinguished professor from until He has supervised at least 13 doctoral theses and three postdoctoral fellows.
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Ebin AMS Chelsea Publishing: An Imprint of the American Mathematical Society The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature.
Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6—9 deal with many of the most relevant contributions to the subject in the years to Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry.
Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field. Readership Graduate students and research mathematicians interested in Riemannian manifolds.
To conclude, one can say that this book presents many interesting and recent results of global Riemannian geometry, and that by its well composed introductory chapters, the authors have managed to make it readable by non-specialists.
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