Peter Petersen

eBook, PDF

Riemannian Geometry (eBook, PDF)

Beschreibung

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research.

Important additions to this new edition include:

- A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise

- An increased number of coordinate calculations of connection and curvature

- General fomulas for curvature on Lie Groups and submersions

- Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger

- Several recent results about manifolds with positive curvature

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 3.34MB

Barrierefreiheit

• Text-to-Speech

Autor

Peter Petersen is a Professor of Mathematics at UCLA. His current research is on various aspects of Riemannian geometry. Professor Petersen has authored two important textbooks for Springer: Riemannian Geometry in the GTM series and Linear Algebra in the UTM series.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 405
• Erscheinungstermin: 24. November 2006
• Englisch
• ISBN-13: 9780387294032
• Artikelnr.: 43729226

Rezensionen

"This is a very advanced textbook on metric and algebraic proofs of critical theorems in the field of metric spaces involving manifolds and other 3D structures. ... First, definitions, theorems, proofs, and exercises abound throughout every section of this 500 page mathematics book. The history of development in the area is comprehensive. ... The experts will find this a useful research tool. ... I recommend this book for researchers having a strong background to begin with." (Joseph J. Grenier, Amazon.com, June, 2016)

From the reviews of the second edition:

P. Petersen

Riemannian Geometry

"A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics."

-EUROPEAN MATHEMATICAL SOCIETY

"This is an introduction to modern methods in Riemannian geometry containing interesting and original approaches to many areas in this field. ... After a general introduction (metrics, curvature, geodesics) and concrete calculations for many examples, the second half of the book considers Bochner-Cartan techniques and comparison geometry. Particularly for these aspects it continues to play an outstanding role among textbooks in Riemannian geometry." (M. Kunzinger, Monatshefte für Mathematik, Vol. 154 (1), May, 2008)

P. Petersen Riemannian Geometry "A nice introduction to Riemannian geometry, containing basic theory as well as several advanced topics." -EUROPEAN MATHEMATICAL SOCIETY