Four-Dimensional Manifolds and Projective Structure

Four-Dimensional Manifolds and Projective Structure is an introduction to differential geometry and 4-dimensional manifolds, covering set theory, linear algebra, topology, Euclidean geometry, manifold theory, and differential geometry. It also covers Lorentz signature and neutral signature and introduces the holonomy group of a manifold for connections associated with metrics of each of these three possible signatures.

Format: Hardback
Length: 288 pages
Publication date: 11 July 2023
Publisher: Taylor & Francis Ltd

Four-Dimensional Manifolds and Projective Structure serve as an accessible and comprehensive introduction to differential geometry and 4-dimensional manifolds. It can be approached initially as a primer on differential geometry, particularly focusing on 4-dimensional manifolds. Moreover, it serves as a gateway to studying projective structure and relatedness in manifolds.

The book's initial chapters provide a solid foundation in set theory, linear algebra, topology, Euclidean geometry, manifold theory, and differential geometry. These chapters cover essential concepts such as metrics, connections on manifolds, curvature, and the fundamental ideas of manifolds.

Subsequently, the author delves deeper into 4-dimensional manifolds, with a particular emphasis on the positive definite case for the metric. The book comprehensively covers Lorentz signature and neutral signature, providing detailed explanations and utilizing the holonomy group of manifolds to understand connections associated with these signatures.

A brief interlude on some key aspects of geometrical symmetry precedes a comprehensive description of projective relatedness. This encompasses the relationship between two symmetric connections and their associated metrics, which give rise to the same geodesic paths.

The book offers a detailed, straightforward discussion of the basic properties of (4-dimensional) manifolds. It introduces holonomy theory, a fundamental concept in differential geometry, and employs it in a novel and insightful manner. This approach makes the book suitable for postgraduates, researchers, including masters and PhD students, who wish to explore the intricacies of 4-dimensional manifolds and their applications.

By providing a comprehensive and well-organized introduction to these topics, Four-Dimensional Manifolds and Projective Structure serves as an invaluable resource for anyone seeking to delve into the world of differential geometry and manifolds.

Weight: 690g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367900427