D. Bao, S. -S. Chern, Z. Shen

eBook, PDF

An Introduction to Riemann-Finsler Geometry (eBook, PDF)

Beschreibung

In Riemannian geometry, measurements are made with both yardsticks and protractors. These tools are represented by a family of inner-products. In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms. So ardsticks are assigned but protractors are not. With such a limited tool kit, it is natural to wonder just how much geometry one can uncover and describe? It now appears that there is a reasonable answer. Finsler geometry encompasses a solid repertoire of rigidity and comparison theorems, most of them founded upon a fruitful analogue of the sectional curvature. There is also a bewildering array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. This book focuses on the elementary but essential items among these results. Much thought has gone into making the account a teachable one.

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Autor

PRELIMINARY TEXT. DO NOT USE. Finsler geometry is a metric generalization of Riemannian geometry and has become a comparatively young branch of differential geometry. Although Finsler geometry has its genesis in Riemann's 1854 "Habilitationsvortrag," its systematic study was not initiated until 1918 by Finsler, and the fundamentals were not completely formulated until the mid-thirties. Later, however, the field underwent a rapid development by mathematicians and physicists of many countries. The main purpose of this book is to study the metric geometry of Finsler manifolds. Portions of the book generalize some standard concepts from Riemannian geometry to the Finsler setting, while other

Produktdetails

• Verlag: Springer US
• Seitenzahl: 435
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461212683
• Artikelnr.: 43993273

Rezensionen

"This book offers the most modern treatment of the topic and will attract both graduate students and a broad community of mathematicians from various related fields."
EMS Newsletter, Issue 41, September 2001