Shaoqiang Deng

Homogeneous Finsler Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book is a unique addition to the existing literature in the field of Finsler geometry. This is the first monograph to deal exclusively with homogeneous Finsler geometry and to make serious use of Lie theory in the study of this rapidly developing field. The increasing activity in Finsler geometry can be attested in large part to the driving influence of S.S. Chern, its proven use in many fields of scientific study such as relativity, optics, geosciences, mathematical biology, and psychology, and its promising reach to real-world applications. This work has potential for broad readership; it is a valuable resource not only for specialists of Finsler geometry, but also for differential geometers who are familiar with Lie theory, transformation groups, and homogeneous spaces. The exposition is rigorous, yet gently engages the reader-student and researcher alike-in developing a ground level understanding of the subject. A one-term graduate course in differential geometry and elementary topology are prerequisites.

In order to enhance understanding, the author gives a detailed introduction and motivation for the topics of each chapter, as well as historical aspects of the subject, numerous well-selected examples, and thoroughly proved main results. Comments for potential further development are presented in Chapters 3-7. A basic introduction to Finsler geometry is included in Chapter 1; the essentials of the related classical theory of Lie groups, homogeneous spaces and groups of isometries are presented in Chapters 2-3. Then the author develops the theory of homogeneous spaces within the Finslerian framework. Chapters 4-6 deal with homogeneous, symmetric and weakly symmetric Finsler spaces. Chapter 7 is entirely devoted to homogeneous Randers spaces, which are good candidates for real world applications and beautiful illustrators of the developed theory.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 242
• Erscheinungstermin: 1. August 2012
• Englisch
• ISBN-13: 9781461442448
• Artikelnr.: 37796661

Inhaltsangabe

Preface.- Acknowledgements.- 1. Introduction to Finsler Geometry.- 2. Lie Groups and Homogenous Spaces.- 3. The Group of Isometries.- 4. Homogeneous Finsler Spaces.- 5. Symmetric Finsler Spaces.- 6. Weakly Symmetric Finsler Spaces.- 7. Homogeneous Randers Spaces.- References.- Index.

Rezensionen

From the reviews: "The aim of the present book is to introduce the aspects of Finsler geometry that can be expressed in terms of Lie theory, having as permanent example the case of homogeneous/symmetric Riemannian manifolds. In this way, new very interesting facts are produced by non-Riemannian tools and geometrical objects like flag and S-curvature. ... this book will be of great interest for a large number of geometers." (Radu Miron, Zentralblatt MATH, Vol. 1253, 2013)