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  1. Bog
  2. Geometri
  3. Differential- og Riemannsk geometri

Differential Geometry and Homogeneous Spaces

Af: Kai Kohler Engelsk Paperback

Differential Geometry and Homogeneous Spaces

Af: Kai Kohler Engelsk Paperback
Tjek vores konkurrenters priser

This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity.

Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincaré–Hopf and Chern–Gauss–Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material.

The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.

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Tjek vores konkurrenters priser

This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity.

Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincaré–Hopf and Chern–Gauss–Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material.

The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 292
ISBN-13: 9783662697207
Indbinding: Paperback
Udgave:
ISBN-10: 3662697203
Kategori: Differential- og Riemannsk geometri
Udg. Dato: 30 okt 2024
Længde: 18mm
Bredde: 235mm
Højde: 156mm
Forlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Oplagsdato: 30 okt 2024
Forfatter(e): Kai Kohler
Forfatter(e) Kai Kohler

Kategori Differential- og Riemannsk geometri

ISBN-13 9783662697207

Sprog Engelsk

Indbinding Paperback

Sider 292

Udgave

Længde 18mm

Bredde 235mm

Højde 156mm

Udg. Dato 30 okt 2024

Oplagsdato 30 okt 2024

Forlag Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

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