The Geometry of Spherically Symmetric Finsler Manifolds
This book presents properties, examples, rigidity theorems and classification results of such Finsler metrics. In particular, this book introduces how to investigate spherically symmetric Finsler geometry using ODE or PDE methods. Spherically symmetr
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Enli Guo · Xiaohuan Mo
The Geometry of Spherically Symmetric Finsler Manifolds
123
SpringerBriefs in Mathematics Series editors Nicola Bellomo Michele Benzi Palle Jorgensen Tatsien Li Roderick Melnik Otmar Scherzer Benjamin Steinberg Lothar Reichel Yuri Tschinkel George Yin Ping Zhang
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Enli Guo • Xiaohuan Mo
The Geometry of Spherically Symmetric Finsler Manifolds
123
Enli Guo College of Applied Sciences Beijing University of Technology Beijing, Beijing, China
Xiaohuan Mo School of Mathematical Sciences Peking University Beijing, Beijing, China
ISSN 2191-8198 ISSN 2191-8201 (electronic) SpringerBriefs in Mathematics ISBN 978-981-13-1597-8 ISBN 978-981-13-1598-5 (eBook) https://doi.org/10.1007/978-981-13-1598-5 Library of Congress Control Number: 2018948827 Mathematics Subject Classification: 53B40, 53C60, 58E20 © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd., part of Springer Nature 2018 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. 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. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Dedicated to the memory of Professor Shiing-Shen Chern
Preface
Spherically symmetric Finsler manifolds are manifolds with spherically symmetric Finsler metrics. Let Ω ⊆ Rn is a rotation symmetric domain and F is defined on Ω. F is said to be
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