L. E. J. Brouwer Collected Works

Geometry, Analysis, Topology and Mechanics

Hans Freudenthal

• Publisher: North Holland
• Year: 2014
• Print ISBN: 9780444106438
• eBook ISBN: 9781483257549
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

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