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Four-Dimensional Manifolds and Projective Structure
Af: Graham Hall Engelsk Hardback
SPAR
kr 212
Four-Dimensional Manifolds and Projective Structure
Af: Graham Hall Engelsk Hardback

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.
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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.
Produktdetaljer
Sprog: Engelsk
Sider: 288
ISBN-13: 9780367900427
Indbinding: Hardback
Udgave:
ISBN-10: 0367900424
Kategori: Algebra
Udg. Dato: 11 jul 2023
Længde: 0mm
Bredde: 234mm
Højde: 156mm
Oplagsdato: 11 jul 2023
Forfatter(e): Graham Hall
Forfatter(e) Graham Hall


Kategori Algebra


Sprog Engelsk


Indbinding Hardback


Sider 288


Udgave


Længde 0mm


Bredde 234mm


Højde 156mm


Udg. Dato 11 jul 2023


Oplagsdato 11 jul 2023

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