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L. E. J. Brouwer Collected Works
Geometry, Analysis, Topology and Mechanics
Hans Freudenthal
- 734 pages
- English
- PDF
- Only available on web
L. E. J. Brouwer Collected Works
Geometry, Analysis, Topology and Mechanics
Hans Freudenthal
About This Book
L. E. J. Brouwer Collected Works, Volume 2: Geometry, Analysis, Topology, and Mechanics focuses on the contributions and principles of Brouwer on geometry, topology, analysis, and mechanics, including non-Euclidean spaces, integrals, and surfaces. The publication first ponders on non-Euclidean spaces and integral theorems, lie groups, and plane transition theorem. Discussions focus on remarks on multiple integrals, force field of the non-Euclidean spaces with negative curvature, difference quotients and differential quotients, characterization of the Euclidean and non-Euclidean motion groups, and continuous one-one transformations of surfaces in themselves. The book also takes a look at vector fields on surfaces and new methods in topology, including continuous vector distributions on surfaces and orthogonal trajectories of the orbits of a one parameter plane projective group. The book then ponders on mechanics and topology of surfaces, as well as the motion of a particle on the bottom of a rotating vessel under the influence of gravitational force. The publication is a valuable reference for researchers interested in geometry, topology, analysis, and mechanics.
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Table of contents
- Front Cover
- Geometry, Analysis, Topology and Mechanics
- Copyright Page
- Table of Contents
- PREFACE
- THE LIFE OF L.E.J. BROUWER
- BIBLIOGRAPHY
- CHAPTER 1. Non-euclidean spaces and integral theorems
- CHAPTER 2. Lie groups
- CHAPTER 3. Toward the plane translation theorem
- CHAPTER 4. Vector fields on surfaces
- CHAPTER 5. Gantor—Schoenflies style topology
- CHAPTER 6. The new methods in topology
- CHAPTER 7. Topology of surfaces
- CHAPTER 8. Mechanics
- ABBREVIATIONS
- LITERATURE