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Chapman and Hall/CRC Four-Dimensional Manifolds and Projective Structure

Name: Four-Dimensional Manifolds and Projective Structure
Brand: Chapman and Hall/CRC
Price: 101.2 GBP
Availability: InStock

Algebra

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Description

Four-Dimensional Manifolds and Projective Structure may be considered ﬁrst as an introduction to diﬀerential geometry and, in particular, to 4-dimensional manifolds, and secondly as an introduction to the study of projective structure and projective relatedness in manifolds. The initial chapters mainly cover the elementary aspects of set theory, linear algebra, topology, Euclidean geometry, manifold theory and differential geometry, including the idea of a metric and a connection on a manifold and the concept of curvature. After this, the author dives deeper into 4-dimensional manifolds and, in particular, the positive definite case for the metric. The book also covers Lorentz signature and neutral signature in detail and introduces, and makes use of, the holonomy group of such a manifold for connections associated with metrics of each of these three possible signatures. A brief interlude on some key aspects of geometrical symmetry precedes a detailed description of projective relatedness, that is, the relationship between two symmetric connections (and between their associated metrics) which give rise to the same geodesic paths. Features: Offers a detailed, straightforward discussion of the basic properties of (4-dimensional) manifolds. Introduces holonomy theory, and makes use of it, in a novel manner. Suitable for postgraduates and researchers, including master’s and PhD students.

Product Specifications

Brand: Chapman and Hall/CRC
Format: hardcover
ASIN: 0367900424
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 11 July 2023
Listed Since: 21 December 2022

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Chapman and Hall/CRC Four-Dimensional Manifolds and Projective Structure

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