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Differential Geometry von Loring W. Tu (2017, Gebundene Ausgabe)

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Produktinformation

This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern-Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss-Bonnet theorem. Exercises throughout the book test the reader's understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.

Produktkennzeichnungen

ISBN-10
3319550829
ISBN-13
9783319550824
eBay Product ID (ePID)
233850389

Produkt Hauptmerkmale

Produktart
Lehrbuch
Sprache
Englisch
Anzahl der Seiten
Xvii Seiten
Verlag
Springer-Verlag Gmbh, Springer International Publishing
Publikationsname
Differential Geometry
Autor
Loring W. Tu
Format
Gebundene Ausgabe
Erscheinungsjahr
2017

Zusätzliche Produkteigenschaften

Hörbuch
No
Inhaltsbeschreibung
Book
Item Length
24cm
Item Height
2cm
Item Width
17cm
Nummer Innerhalb der Serie
275
Item Weight
747g
Buchreihe
Graduate Texts in Mathematics

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Differential Geometry von Loring W. Tu (2017, Gebundene Ausgabe)

About this product

Produktinformation

Produktkennzeichnungen

Produkt Hauptmerkmale

Zusätzliche Produkteigenschaften

Best Selling in Adult Learning & University

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