Background
Ebin, David Gregory was born on October 24, 1942 in Los Angeles, California, United States. Son of Norman and Elizabeth (Nimiec) Ebin.
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book
Comparison Theorems in Riemannian Geometry (Ams Chelsea Publishing)
(The central theme of this book is the interaction between...)
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. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. 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 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. 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 1975. 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.
http://www.amazon.com/gp/product/0821844172/?tag=2022091-20
Comparison Theorems in Riemannian Geometry byG. Ebin
http://www.amazon.com/gp/product/B004M1VQTW/?tag=2022091-20
Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) by Jeff Cheeger and David G. Ebin (2008-08-04)
http://www.amazon.com/gp/product/B01FIWIWUO/?tag=2022091-20
David Gregory Ebin
Edit Profileeducator mathematician researcher
Education
AB, Harvard College, 1964; Doctor of Philosophy, Massachusetts Institute of Technology, 1967.
Career
Lecturer, University of California, Berkeley, 1967-1969; associate professor mathematics, State University of New York, Stony Brook, 1969-1978; professor mathematics, State University of New York, Stony Brook, since 1978; Adjunct Professor applied mathematics, State University of New York, Stony Brook, since 1989. Editor American Mathematics Society Proceedings, Providence, Rhode Island, 1983-1988.
Achievements
Works
book
-
Comparison Theorems in Riemannian Geometry (Ams Chelsea Publishing)
(The central theme of this book is the interaction between...)
- Comparison Theorems in Riemannian Geometry byG. Ebin
- Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) by Jeff Cheeger and David G. Ebin (2008-08-04)
-
Comparison Theorems in Riemannian Geometry (Ams Chelsea Publishing)
Connections
Married Barbara J. Burkhard, June 6, 1971. Children: Hannah Rebekah, Jacob Benjamin, Zachary Israel, Abigail Cilia.
