How Long to Read Dirac Operators in Riemannian Geometry

How Long Does it Take to Read Dirac Operators in Riemannian Geometry?

It takes the average reader 3 hours and 35 minutes to read Dirac Operators in Riemannian Geometry by Thomas Friedrich

Assuming a reading speed of 250 words per minute. Learn more

Description

For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants. In this text, Friedrich examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of spin structures and $\textrm{spin}mathbb{C}$ structures. With this foundation established, the Dirac operator is defined and studied, with special attention to the cases of Hermitian manifolds and symmetric spaces. Then, certain analytic properties are established, including self-adjointness and the Fredholm property. An important link between the geometry and the analysis is provided by estimates for the eigenvalues of the Dirac operator in terms of the scalar curvature and the sectional curvature. Considerations of Killing spinors and solutions of the twistor equation on M lead to results about whether M is an Einstein manifold or conformally equivalent to one. Finally, in an appendix, Friedrich gives a concise introduction to the Seiberg-Witten invariants, which are a powerful tool for the study of four-manifolds. There is also an appendix reviewing principal bundles and connections. This detailed book with elegant proofs is suitable as a text for courses in advanced differential geometry and global analysis, and can serve as an introduction for further study in these areas. This edition is translated from the German edition published by Vieweg Verlag.

How long is Dirac Operators in Riemannian Geometry?

Dirac Operators in Riemannian Geometry by Thomas Friedrich is 213 pages long, and a total of 53,889 words.

This makes it 72% the length of the average book. It also has 66% more words than the average book.

How Long Does it Take to Read Dirac Operators in Riemannian Geometry Aloud?

The average oral reading speed is 183 words per minute. This means it takes 4 hours and 54 minutes to read Dirac Operators in Riemannian Geometry aloud.

What Reading Level is Dirac Operators in Riemannian Geometry?

Dirac Operators in Riemannian Geometry is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Dirac Operators in Riemannian Geometry?

Dirac Operators in Riemannian Geometry by Thomas Friedrich is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

To buy Dirac Operators in Riemannian Geometry by Thomas Friedrich on Amazon click the button below.