Homogeneous Finsler Spaces: Springer Monographs in Mathematics
Autor Shaoqiang Dengen Limba Engleză Paperback – 19 sep 2014
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Paperback (1) | 638.43 lei 6-8 săpt. | |
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Hardback (1) | 644.63 lei 6-8 săpt. | |
Springer – aug 2012 | 644.63 lei 6-8 săpt. |
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Specificații
ISBN-13: 9781489994769
ISBN-10: 1489994769
Pagini: 256
Ilustrații: XIV, 242 p.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.36 kg
Ediția:2012
Editura: Springer
Colecția Springer
Seria Springer Monographs in Mathematics
Locul publicării:New York, NY, United States
ISBN-10: 1489994769
Pagini: 256
Ilustrații: XIV, 242 p.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.36 kg
Ediția:2012
Editura: Springer
Colecția Springer
Seria Springer Monographs in Mathematics
Locul publicării:New York, NY, United States
Public țintă
ResearchCuprins
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.
Recenzii
From the reviews:
“The main purpose of this book is to show how ideas from Lie theory have spread to Finsler geometry. This book is the first one in the field of homogeneous Finsler spaces. … Finsler geometry has been developing rapidly, but this book may give a new spirit to Finsler geometry from the view of Lie theory, and it can be highly recommended to anyone who wants to study Finsler geometry from this point of view.” (Hamid Reza Salimi Moghaddam, Mathematical Reviews, June, 2013)
“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)
“The main purpose of this book is to show how ideas from Lie theory have spread to Finsler geometry. This book is the first one in the field of homogeneous Finsler spaces. … Finsler geometry has been developing rapidly, but this book may give a new spirit to Finsler geometry from the view of Lie theory, and it can be highly recommended to anyone who wants to study Finsler geometry from this point of view.” (Hamid Reza Salimi Moghaddam, Mathematical Reviews, June, 2013)
“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)
Textul de pe ultima copertă
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.
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.
Caracteristici
Presents the most recent results on the applications of Lie theory to Finsler geometry Provides an accessible introduction to Finsler geometry that allows the reader to quickly understand topics and to access related problems Contains related work concerning Randers spaces, making it suitable for readers with a background in biology, as well as various topics for readers with backgrounds in pure algebra? Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras