Homogeneous Finsler Spaces
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 fie
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For further volumes: http://www.springer.com/series/3733
Shaoqiang Deng
Homogeneous Finsler Spaces
123
Shaoqiang Deng School of Mathematical Sciences Nankai University Tianjin People’s Republic of China
ISSN 1439-7382 ISBN 978-1-4614-4243-1 ISBN 978-1-4614-4244-8 (eBook) DOI 10.1007/978-1-4614-4244-8 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012942472 © Springer Science+Business Media New York 2012 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to the memory of Professor Shiing-Shen Chern on the occasion of the centenary of his birth
Preface
In recent years, Finsler geometry has been developing rapidly. There are two main reasons for this development. First, the influence of S.S. Chern in the late twentieth century was enormous; his guidelines rapidly accelerated both interest and results, first in the United States, including David Bao, Zhongmin Shen, as well as other mathematicians, and then in China. Today, a large group of young and talented mathematical researchers all over the world are working on specific issues in this field. Second, new areas of application arose in the 1980s (R.S. Ingarden, P.L. Antonelli, among others) in biology, optics, quantum physics, and also in psychology, geosciences,
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